Cohomology of simple modules for algebraic groups

Show simple item record

dc.contributor.author Ibraev, Sh.Sh.
dc.contributor.author Kainbaeva, L.S.
dc.contributor.author Menlikhozhayeva, S.K.
dc.date.accessioned 2020-04-19T07:21:27Z
dc.date.available 2020-04-19T07:21:27Z
dc.date.issued 2020-01-30
dc.identifier.citation Ibraev Sh.Sh. Cohomology of simple modules for algebraic groups/Sh.Sh. Ibraev, L.S. Kainbaeva, S.K. Menlikhozhayeva//Қарағанды универисетінің хабаршысы. Математика Сериясы.=Вестник Карагандинского университета. Серия Математика.=Bulletin of the Karaganda University. Mathematics Series.-2020.-№1(97).-P. 37-43. ru_RU
dc.identifier.issn 2663-4872
dc.identifier.uri http://rep.ksu.kz//handle/data/9682
dc.description.abstract In this paper, we consider questions related to the study of the cohomology of simple and simply connected algebraic groups with coefficients in simple modules. There are various calculating methods for them. One of the effective methods is to study the properties of the Lyndon–Hochschild–Serre spectral sequence with respect to the infinitesimal subgroup, the Frobenius kernel of a given algebraic group, and the properties of various cohomological sequences. We have studied the properties of various short exact and corresponding long exact cohomological sequences of modules over an algebraic group associated with simple modules with highest restricted weights. Some properties of the cohomology of the Frobenius kernel with coefficients in simple modules with higher restricted weights are described. We also studied the properties of the Lyndon– Hochschild–Serre spectral sequence on the first quadrant for simple modules with highest restricted weights. The limiting values of the points of the first quadrant of the spectral sequence are described. It is proved that for the simple, simply connected algebraic group G over an algebraically closed field k of characteristic p > h with an irreducible root system R and for a simple G-module V with restricted highest weight, there is an isomorphism of G-modules Hj(G; V ) = HomG(k;Hj(G1; V )(􀀀1)) for all j 0; where G1 is the Frobenius map kernel for G; h is the Coxeter number of the root system R: This isomorphism allows us to reduce the calculation of the cohomology of group G with coefficients in simple modules with higher restricted weights to the calculation of the corresponding cohomology of the Frobenius kernel G1: ru_RU
dc.language.iso en ru_RU
dc.publisher KSU publ. ru_RU
dc.relation.ispartofseries Mathematics Series;№1(97)
dc.subject algebraic group ru_RU
dc.subject Chevalley group ru_RU
dc.subject representation of Lie group ru_RU
dc.subject Frobenius kernel ru_RU
dc.subject simple module ru_RU
dc.title Cohomology of simple modules for algebraic groups ru_RU
dc.type Article ru_RU


Files in this item

This item appears in the following Collection(s)

Show simple item record

Search DSpace


Browse

My Account