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Since a basis for a Free Lie Algebra $\cal{FL}$ with n generators $x_1,\ldots x_r$ can be described by the elements $\{ [\ldots[x_{i_1},x_{i_2}]x_{i_2}\ldots]x_{i_m}] , 1 \leq x_{i_j} \leq r , 1 \leq j \leq m , m \in \mathbb{N} \}$ , what is the point of using the Hall basis for $\cal{FL}$? Both basis generate the same graded algebra and the first basis is simpler than the Hall basis .
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closed as off-topic by Ricardo Andrade, Daniel Moskovich, Jack Huizenga, Andrey Rekalo, Stefan Kohl Dec 1 '13 at 9:22This question appears to be off-topic. The users who voted to close gave this specific reason:
Your elements don't form a basis. You haven't given any conditions on the indices $i_j$, so $[x_1,x_1]$ is in your list, but it is zero. Now consider words of length three. Among these are $[[x_1,x_2],x_3]$, $[[x_2,x_3],x_1]$ and $[[x_3,x_1],x_2]$. The sum of these three is zero by the Jacobi identity, so they are not linearly independent. You might want to insist that the list of indices $i_1,\dotsc,i_r$ is strictly increasing, but then $[[x_2,x_3],x_1]$ would not be in the span. |

subset: commoncrawl


text:
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From restaurant website: "Upon his arrival to Vancouver it was no surprise not only that Michel would open his own fine dining French restaurant but, that he would also name it after the finest restaurant he had ever seen and dined at in his hometown of Strasbourg...the 3 star Michlelin restaurant - Au Crocodile. Chef/owner Emile Jung had instilled a level of quality and service that Michel had to duplicate for himself and Vancouverites alike. Michel's main goal was to open a restaurant that could match and achieve the level of culinary standards and service that are still present today at Au Crocodile. Twenty-two years have passed and it is safe to say that Michel has surpassed all expectations. Vancourites are pleased he Michel followed his dream."
I was there a couple weeks ago and waited forever (45 minutes) to be served. Bread was not given to us for almost an hour and they weren't even busy. I was really disappointed. It was my second time there. Nobody acknowledged our existence until the hostess noticed that nobody came to us. The food was as advertised, I'm glad they got something right! We just sat there and kept our eyes on the clock to see when our food would be placed on the table. I feel that this restaurant is overrated. I might go back again someday if the reviews here and from others change my mind.
My wife and I, after much research on the internet, to find the perfect French restaurant for our anniverary settled on "le crocodile" based on the reviews. We were not disappointed. The food was excellent and the service was outstanding. The staff was welcoming from the moment we walked in. The price was, we felt, very reasonable. We had a three course meal with a bottle of wine and a martini to start and were quite full. The portions were of good size. This will be our special occasion restaurant from now on. I would recommend this to anyone looking for a nice, romantic evening with good food.
The first time my husband and I went to Le Crocodile it was with a wedding present gift certificate. The experience was so good, we have this restaurant on our top-three list! The service is great, especially the wine consultant. I don;t even read the menu - order from the extesive list of Features your waiter will read out. There is usually elk or caribou meat, which is fantastic every time I've ordered! I can't say enough good things about this place, except GO!
I have been fortunate enough to eat at some of the best restaurants around the world. Le Crocodile has lived up to the mark and has never disappointed me. I am taken there for birthdays and anniversaries and in turn take others as a special. (I also frequent other eateries and will include those reviews soon.)
The fois gras is poetic and although I fancy myself as a gourmet cook, that dish is simply too complicated to duplicate in a home kitchen successfully. It was silky and ethereal. The sweetbreads were fabulous and when I gave one "as a taste" to my young guest he nearly swooned. (University student son, doesn't get out much :)
It was if anything almost too much and we had no room for dessert. DO bring a fat wallet because it is not cheap. As an aniversary dinner or a place to propose (I witnessed it twice) it can't be beat.
This place might be over rated. The food LOOKS tasty but the portions are sample size. For the portions you receive, the prices are not justified. The service was pleasant. Great place to impress your date. However, be prepared to eat again, shortly after...
A while ago I went to Le Crocodile with my family. When we came in, it was quite busy so we were put into a corner. Although some people may not like this, I love corners of restaurants as they are very cozy. For dinner I had the duck breast with froie gras. It was exquisite. The froie gras was creamy and the duck breast was tender but not to chewy. As almost all French food, wine was incorporated into the dish as a sauce; a delicious one I might add.
The duck came with a bit of steamed vegetables on a separate plate. Unfortunately, though the duck and froie gras were outstanding, the vegetables were forgettable. However, it is hard to find a restaurant who can make steamed vegetable unforgettable, yet it has been done, and therefore, the food for Le Crocodile, dose not get a 5 out of 5.
I had a taste of my families dishes, and they were very delicious. The beurre blanc was creamy and smooth, with a bit of a tang, which comes from what I suspect is white wine vinegar. Finally, the risotto was one of the best risottos I've ever tasted.
For desert I had a chocolate crepe. The main course was amazing but the desert was lacking. Although the chocolate crepe was delicious, it was nothing out of the ordinary.
Despite what I have said above, the food was delicious in all aspects. Though I did criticize the vegetables, and desert, it does not mean that they are not delicious, it is just that they are not incredible, like some of there other food.
Le Crocodile is a great place for French food, and a great place for food lovers. Gourmands everywhere (even if French food is not there favourite) will be able to appreciate the food at Le Crocodile.
Bon Appetite!
If you decide to go to Le crocodile, be sure. No surprise. The food is amazing. Fisrt class. Appies, main course, desserts and wine list. one hundred per cent excellent. Doesn't matter if seafood, poultry or tenderloin, all good, better, all incredible. The service is good too but not that impressive. If you have visitor out of town, go Crocodile. No mistakes.
A couple of friends and myself decided to splurge for a meal and picked this restaurant, as it has been in the back of our minds for a while.
When we arrived, we were promptly seated and were handed the cocktail list first. We ordered some drinks and waited for the menus. It was a little strange, but it appears that they let you drink your cocktails first before they will present the menus to you. We did eventually get them and everything was fine from that point on.
I've never had frog legs before, so we decided to split an order. They were served with a rich garlic butter sauce, that gave them an excellent flavour. I opted for the onion tart for my main appetizer and it was excellent. My friends had the soft shell crab salad and the tuna/crab meat salad. They both enjoyed their appetizers, though eating the shell of the crab took a little getting used to for my friend.
For our mains, I had the surf and turf special, which consisted of a sirloin steak with 3 prawns. The steak was made quite well, but the prawns seemed a bit on the small side. One friend had the caribou special, which he found quite tasty especially with the red wine reduction sauce. The other had the arctic char and he finished off the plate.
Finally, we came to the desserts. We were accidentally presented with the cocktail menus again by mistake and had to flag down the waiter to get the right menus. Once we got it, I decided to go with the Pear tart. It was served with vanilla ice cream and it was very nice. The other desserts ordered were the Peaches soaked in Ice Wine and the fresh strawberries. Both were well received.
Overall, everything was great. Service was a little strange with the menus, but was good overall. The number of items on the menu made it a little difficult to finally decide on what to order. When we have the opportunity to splurge again, we will definitely consider Le Crocodile again.
Our first, and surely not the last, experience at le Crocodile was really good. The service was superb. Out server was charming and very knowledgeable. From the moment we walked in we were greeted with courtesy and felt welcome. The restaurant was packed by 9pm on a Thursday night. People seemed to be really enjoying themselves. I enjoyed a main course of caribou in a pinot noir reduction prepared to a medium-rare. Attention to detail in both flavour and presentation seem to be the hallmark le Crocodile. For desert I shared crepes au chocolate. It was good, but by no means outstanding. Overall the food is very fresh and leaves your palate feeling clean and satisfied. The wine list definitely caters to a discerning taste and strong economy.
We have enjoyed few meals at the Crocodile. It's brasserie look is welcoming and the service is impeccable.
We were impressed by the quality of the food although it is more a traditional, classical cuisine. This classicism is perhaps what seduces number of patrons but the Alsacian food tradition -hearty food- made me wonder for more delicate and subtle tastes.
The wine list is fine and this is the perfect spot for a business lunch between civilized people.
The Crocodile will never disappoint and still is reasonably priced.
Vancouver is blessed to have such a classic.
Went here for dinner with my boyfriend, was quite busy for a Tuesday night.
Waitress was quite informative on the specials.
I had the Veal chop, was alright... i had ordered it medium rare, some parts were a little over cooked and some parts were a little raw which i found odd, the shitakes they added tasted off to me. Boyfriend had the Baked salmon which was amazing! wish i had that :( haha. You can also special order whole cakes which was a pleasant surprise.
In the end you can't pay with debit which we found surprising, so the boyfriend left me sitting alone for about 15 minutes while he looked for an atm, a waiter had offered to sit with me while i waited though haha.
Overall would go back, but would bring cash lol
Le Crocodile is *amazing*. The food, the service - absolutely top notch. I can recommend this restaurant without hesitation.
We ordered the from the chef's menu which changes every week. The menu had so many courses and so much variety and dazzled me with such fantastic flavors that ironically, I honestly cannot remember all the details.
I remember snow crab legs AND lobster ravioli where I mopped up every last drop of mouth watering cream sauce.
I remember tender veal in a fragrant Au Jus.
I remember being so full and satisfied that I swore I couldn't eat another bite - but when desert came - a luscious slice of pistachio cake, I couldn't resist.
The chef's menu is a little pricey ($75.00) and whether *any* single meal could be worth is still a question I wrestle with - but chef's menu at Le Crocodile comes darned close to making me say YES.
I needed to make my praise of Le Crocodile clear right up front because I was going to rant about "fine dining". These days, the notion of fine dining almost makes me cringe. Look at my reviews of The Observatory or the C restaurant. Add to that many other "fine" dining experiences that barely qualified as mediocre that I couldn't find the energy to bother reviewing.
It seems that to many (dare I say MOST) fine dining establishments, "fine dining" means three things: Pretentious. Small Portions. Expen$ive. Notice that fine flavorful food is NOT a requirement. Most of the cooks for these restaurants should be relegated to McDonalds to *upgrade* their skills.
But Le Crocodile is... it's just beautiful. It's great food. It's great service. It is everything that fine-dining should be. Try it, you will not be disappointed.
I was brought here by a friend for my birthday! What a surprise, as soon as we walked in they knew it was my birthday. They make some very special touches and trying to personalize my experience which was great! The food is truly classic french, even the plating, but its great food, and a great experience! I had the seafood tempure salad to start. The pan seared duck with calvados jus. amazing and the side plate of vegetable it was place like an art piece. wonderful. perfectly cooked. service was good.
However there drink are mediocre, needs more improvement with there bartender.
We came to celebrate our 2yr anniversary at le crocodile...1st things first if you drive valet, it is easier and cheaper than parking on the street for two hours;valet $7 I recall. I have always wanted to check this place out! Now not just me but WE are glad we did. For a fine dinning restaurant the prices were reasonable, the plating was neat and tidy the portions were very adequate. Major thumbs up and great reason to come back was the Steak tartar it was amazing I want some right now just thining about it. The crab cake special was alright; I really enjoyed the salmon 3 ways smoked, tartar and candied. Again the tartar was A#1 the smoked good and the candied was alright. The goat cheese salad with endive was awesome and they do not skimp on the goat cheese it was plentyful. We also had the french onion soup, it was so so. Entrees: I had the duck mid rare it was fair I enjoyed it but not worth aordering again. Next time I would most likely get the lobster a real great value at $42, you get 1 1/2 pounds shelled! My wife had the sablefish it was solid I would order that again. We finished with coffee and dessert Crepes aux Chocolat, Mousse Noisette, Chocolat ChaudChocolate Crepes, Hazelnut Mousse filling, Warm Chocolate and Orange Ice Cream it was recommeded bt our wiatier. Dessert was outstanding. All in all we would return..our server William was very knowledgeable and a great host as well.
I took my wife here last night for our 1st anniversary after a co-worker was constantly raving about the place. I have to say it was the best dining experience my wife and I ever had.
Our server Simon was great. He was very friendly and very attentive as our glasses were always topped up. Throughout the dinner the maitre d' came over a couple times to make sure everything was ok as did the sommelier to ask how our wine was.
For starters I had the arugula and prawn salad and my wife had the pan seared goat cheese on endive salad. Both were delicious. Second, I had the frog legs and my wife the fois gras special. This was the first time eating frog legs and I thought were absolutely fabulous. The portion was much bigger than I thought it would be. The garlice butter sauce was amazing and the frog legs were cooked perfectly. My wife's fois gras was just okay but that's probably because I am not a huge fan of any liver dishes.
For our main course we both had the steamed atlantic lobster. Again, it was delicious. It was cooked and seasoned perfectly and was accompanied by vegetables and a nice rich creamy butter sauce.
We had two bottles of Chablis Premier Cru ($95) which was probably one fo the best white wines I have ever enjoyed. It went down very nice and the fruity flavours lingered nicely on my palate.
Our bill came out to $390 but without any wine would have been $200 which I think is quite reasonable considering the quality of the food and service. I definitely recommend this restaurant for a romantic dinner and I can't wait to go back!
Food - The lobster tempura and scallop salad was fresh and delicious. The flavours were perfect. The frog legs had a beautiful truffle oil flavour. The portions of the mains were HUGE. This is the biggest portion that I've seen for this price at any fine dining restaurant in Vancouver. I had the lamb, and my guest had the prime rib - both delicious.
Service was excellent. Very attentive but not pretentious at all. They paid attention to every detail, but yet did not make you feel like you were being hovered over. Our waiter was very helpful making great recommendations.
We will be back and we will be recommending this restaurant to family and friends!
I came here with my girlfriend for her birthday dinner. When we arrived, I saw a ton of customers inside and was glad I made reservations a week prior. The place was perfectly lit (not too dark or bright) for dinner time. The hostess took our coats and showed us to the table. The waiter was very friendly in explaining any questions we had about menu items. The food was excellent (as I would expect from a pricey place such as this). We ordered and crab cake and French onion soup for appetizer. Both were excellent. For the main course I had a duck dish, which was cooked perfectly tender and tasty. My girlfriend had the rack of lamb, which was also very tender and juicy. For dessert, I had this moist chocolate cake with orange sorbet. My girlfriend didn't want any, but the waiter was smart enough to bring two spoons. When we were leaving the restaurant, the waiter helped us put on our coats with a very honestly delivered thank you. I will definitely recommend this place if you don't mind spending a bit on service and food.
Once great, now tired place that feel like it caters to tourists sent there by bribed concierges. Staff was very friendly. Esoteric wine list designed to impress just adds to the confusion. 15 min. before first drink order taken even though the Maitre d' had reminded us that our table was reserved later. The chefs tasting menu looked great but... Halibut smelled like bleach, Very low quality Foie gras with sinew, (Yep, true), of the three kinds of meat two were tasteless. All in all, steer clear. There are much better choices in Vancouver these days.
You can always depend on receiving top notch service and food here. The servers know their product and have no problems helping you out if you ever need a suggestion on what wine would be ideal. No matter how busy they are (full dining room at lunch time), the food is cooked to perfection. They always serve a little dessert and a little plate of chocolate crocodiles at the end which is a nice touch. I highly recommend this place. Make sure you make a reservation to ensure you won't be disappointed if you can't get in because they do get busy.
My girlfriend treated me to this restaurant for my 34th birthday and, being a connoisseur of French food, this certainly was a treat!
Reservations (which can and should be made ahead of time, and on their website at http://www.lecrocodilerestaurant.com/) were available at near the time we wanted a week ahead of time, and they were quick in confirming reservations. Upon arrival, we were greeted immediately by the hosts and seated. Right on time! This was a busy and packed Saturday night, but we didn't wait at all. Seated by the wall, the two of us had a nice table and, although the other tables were fairly close, the intimate atmosphere of the place made our experience fairly private. The waiter was prompt throughout, as was the bread boy. The maitre d' also stopped by to ask how our food was.
The menu prices were, in my opinion, pretty standard for a good quality French restaurant. I had a roasted free range chicken for $26 and it was a very delicious dish. The mustard sauce was very tasty indeed! My partner ordered a lobster prawn pasta dish and she said it was fairly good.
(The only complaint we had was the $8 bottle of water they charged us for. Yes, it was Evian, but $8? Give me a break.)
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