Cohomology of simple modules for sl3(k) in characteristic 3
Сипаттамасы 3 sl3(k) үшiн жәй модульдердiң когомологиялары
Когомологии простых модулей для sl3(k) в характеристике 3
Ibrayeva A.A. Ibraev Sh.Sh. Yeshmurat G.K.
2021E.A.Buketov Karaganda State University Publish House
Bulletin of the Karaganda University. Mathematics Series
2021#103Issue 336 - 43 pp.
In this paper we calculate cohomology of a classical Lie algebra of type A2 over an algebraically field k of characteristic p = 3 with coefficients in simple modules. To describe their structure, we will consider them as modules over an algebraic group SL3(k). In the case of characteristic p = 3, there are only two peculiar simple modules: a simple that module isomorphic to the quotient module of the adjoint module by the center, and a one-dimensional trivial module. The results on the cohomology of simple nontrivial module are used for calculating the cohomology of the adjoint module. We also calculate cohomology of the simple quotient algebra Lie of A2 by the center.
exact sequence , Lie algebra , restricted module cohomology , simple module
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Korkyt Ata Kyzylorda University, Kyzylorda, Kazakhstan
Korkyt Ata Kyzylorda University
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