Second cohomology group of the finite-dimensional simple Jordan superalgebra D-t, t not equal 0

Gomez Gonzalez F. A.; Ramirez Bermudez J. A.

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Second cohomology group of the finite-dimensional simple Jordan superalgebra D-t, t not equal 0

机译：Second cohomology group of the finite-dimensional simple Jordan superalgebra D-t, t not equal 0

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摘要

The second cohomology group (SCG) of the Jordan superalgebra D-t, t not equal 0, over an algebraically closed field F of characteristic zero is calculated by using the coefficients which appear in the regular superbimodule Reg D-t. Contrary to the case of algebras, this group is nontrivial thanks to the non-splitting caused by the Wedderburn Decomposition Theorem [F. A. Gomez-Gonzalez, Wedderburn principal theorem for Jordan superalgebras I, J. Algebra 505 (2018) 1-32]. First., to calculate the SCG of a Jordan superalgebra we use split-null extension of the Jordan superalgebra and the Jordan superalgebra representation. We prove conditions that satisfy the bilinear forms h that determine the SCG in Jordan superalgebras. We use these to calculate the SCG for the Jordan superalgebra D-t, t not equal 0. Finally, we prove that H-2 (D-t, RegD(t)) = 0 +F-2, t not equal 0.

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《Journal of algebra and its applications》 |2022年第5期|共13页
作者
Gomez Gonzalez F. A.; Ramirez Bermudez J. A.;
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Univ Antioquia;

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正文语种英语
中图分类代数、数论、组合理论;
关键词
Jordan superalgebra; second cohomology group; Wedderburn principal theorem; split null extension; regular superbimodule; decomposition theorem; ALTERNATIVE SUPERALGEBRAS;

Second cohomology group of the finite-dimensional simple Jordan superalgebra D-t, t not equal 0

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