"Floating" desk - Avoiding wood sag, aluminium right angle support
I would not waste time with an aluminium angle iron. It will being next to nothing in terms of real support for the front edge of your desk. Instead you should look at something like steel rectangular tubing. This you would simply fasten to the underside of desk a little back from the front and make sure it was supported on each end. The steel tubing could be painted black to hide or a standout contrast color. Alternatively you could also install an on-edge apron board in front of the tubing to hide it from view entirely. The apron board itself will add additional support.

For your longer span across the top of your diagram I see a length of 2170mm. Use a tubing with a 50mm width and a 100mm height and a wall thickness of 5mm. Such tubing, if supported on each end, should be able easily handle a center load of 100kg with less than 10mm of vertical deflection. 

(I used the deflection calculator here). 

In the corner where you have indicated "strength ???" you will want to arrange to join the two rectangular tubes into a "T" like joint. This could be as simple as drilling some through holes and bolting in a short piece of angle iron in the underside corner. Alternatively you could plan things out and weld the joint if you have that type of equipment available.

I would also purge the idea of the mortise joint and the construction complications that brings. Instead use a flat steel plate that lays across the joint and screw that to the bottom side of the desk surfaces. I could easily envision something 75-100mm wide with a 3-5mm thickness. Two rows of holes pre-drilled into the plate at intervals of 75-100mm should do well to support the edges of the desk. Best would be if its length went as long as feasible from the front edge back to the wall.