### Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 18 (2022), 026, 17 pages      arXiv:2203.16142      https://doi.org/10.3842/SIGMA.2022.026

### Cohomology of $\mathfrak{sl}_3$ and $\mathfrak{gl}_3$ with Coefficients in Simple Modules and Weyl Modules in Positive Characteristics

Sherali Sh. Ibraev
Korkyt Ata Kyzylorda University, Aiteke bie St., 29A, 120014, Kzylorda, Kazakhstan

Received August 12, 2021, in final form March 26, 2022; Published online March 30, 2022

Abstract
We calculate the cohomology of $\mathfrak{sl}_3(k)$ over an algebraically closed field $k$ of characteristic $p>3$ with coefficients in simple modules and Weyl modules. We also give descriptions of the corresponding cohomology of $\mathfrak{gl}_3(k)$.

Key words: Lie algebra; simple module; cohomology.

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