
supergroup (bhautikshastra)

supergroupchi sankalpana mhanje gatache samanyikaran. dusya shabdant, pratyek supargrupmadhye eka naisargik gut rachana asate, parantu dilelya gatala supergroup mhanoon tayar karnyasathi ekapeksha jaast marg asoo shakatat. supergroup haah khotya gatasarkha asato, jyamadhye tyanchyavar paribhashit kelelya gulgulit karyachi eka suspasht kalpana asate. 
tathapi, karyanmadhye summ aanee visham bhag asoo shakatat. shivay, eka supargrupmadhye eka atee asatya bijganit asate, jeey khote gatansathichya khote bijganitasarkhich bhoomika bajavate, jyamadhye teey bahutek pratinidhitva siddhant nishchit karatat aanee vargikaranasathi prarambhik bindu konata aahe.
tapasheel.
adhik aupcharikpane, khote supergroup haah eka supermanifold 'jee' aahe, jyamadhye gunakar morphism sootra _ 1, eka inversion morphism sootra _ 2 aanee eka unit morphism sootra _ 3 aahe, jeey 'jee' laa supermanifoldschya shrenitil eka gut object banavate. yacha arth assa qee, parivartaneey aakruti mhanoon tayar kelele, samoohache nehamiche sahsambandh aanee vyutkram swasiddhant tikoon rahatat. pratyek anekpat haah eka atimanav asalyane, eka khote supergroup khote gut yaa kalpanela samanya karato.
anek sambhavya supergroup aahet. saiddhantik bhautikshastrat sarvadhik rus asalele teey aahet jeey poinker gut kinwa anuroop gut vadhavtat. orthosymplectic gut oo. ess. pii. ("emm") heey vishesh swarasyapoorn aahet."."aine") aanee superunitary gut suu ("" emm "") "."aine").
samatulya bijganitiy drushtikon yaa nirikshanapasun suru hoto qee supermanifold heey tyachya supercommutative smooth functionschya ringdware nirdharit kele jaate aanee supermanifoldsche morphism heey tyanchya viruddha dishene asalelya functionsmadhil bijganita homomorphismshy eka teey ekashi sambandhit aahe, i.eae. supermanifoldschi shreni hii gulgulit shrenibaddha parivartaneey karyanchya algebranchya shrenichya viruddha aahe. laee supergroup paribhashit karananya parivartanatmak aakrutitil serve baana ulat kelyane asey disun yete qee supergroupvaril karyanmadhye zed2-shrenibaddha hopph bijganitachi rachana aahe. tyachpramane yaa hopph bijganitachi pratinidhye zed2-shrenibaddha commodules asalyache nishpann hote. haah hopp bijganit supergroupche jaagtik gunadharm deto.
aanakhi eka sambandhit hopph bijganit aahe joou mageel hopph bijganitacha duheri aahe. mool sthanavaril shrenibaddha vibhedak prachalakanchya hopph bijganitashi teey olakhale jaau shakate. heey fakt samamitiche sthanik gunadharm i dete.eae.heey keval anant atisamiti parivartanambaddal mahitee dete. yaa hopph bijganitachi pratinidhye modules aahet. shrenibaddha nasalelya prakaranapramane, yaa hopph bijganitache varnan purnapane bijganitiyadrushtya khote atee bijganitache sarvatrik aachchadan bijganit mhanoon kele jaau shakate.
ashach prakare ekhadi vyakti affine bijganitiy supergroupchi vyakhya superalgebric affine prakaranchya shrenitil samooh object mhanoon karoo shakate. eka sanlagn bijganitiy atisamuhamadhye tyachya atee bahupadichya hopp bijganitashi eka samaan sambandh asato. jyamiteey aanee bijganitiy drushtikon ektrit karananya yojananchi bhasha vaparoon, bijganitiy supergroup yojana super abelian prakaransah paribhashit kelya jaau shakatat.
udaharane.
super-pointair gut haah superspachya samamiticha gut aahe (visheshtah, formula _ 4 superchargess minkowski superspace, jithe anekada formula _ 4 haah 1 manla jaato). bahutekda tyavar bijganit staravar upchar kele jaatat aanee teey super-pointair bijganitadvare tayar kele jaate.
atee-anaupacharik gut haah atee-anaupacharik bijganitadvare nirman jhalelya atee-jagechya anuroop samamiticha gut aahe.