Second cohomology group of the finite-dimensional simple Jordan superalgebra 𝒟t, t≠0
| Autor: | J. A. Ramírez Bermúdez, F. A. Gómez González |
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| Rok vydání: | 2021 |
| Předmět: |
Pure mathematics
Algebra and Number Theory Group (mathematics) Applied Mathematics Mathematics::Rings and Algebras Astrophysics::Instrumentation and Methods for Astrophysics Zero (complex analysis) Computer Science::Computation and Language (Computational Linguistics and Natural Language and Speech Processing) Cohomology Superalgebra Simple (abstract algebra) Computer Science::General Literature Algebraically closed field Mathematics Decomposition theorem |
| Zdroj: | Journal of Algebra and Its Applications. 21 |
| ISSN: | 1793-6829 0219-4988 |
| DOI: | 10.1142/s0219498822500918 |
| Popis: | The second cohomology group (SCG) of the Jordan superalgebra [Formula: see text], [Formula: see text], over an algebraically closed field [Formula: see text] of characteristic zero is calculated by using the coefficients which appear in the regular superbimodule [Formula: see text]. Contrary to the case of algebras, this group is nontrivial thanks to the non-splitting caused by the Wedderburn Decomposition Theorem [F. A. Gómez-González, 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 [Formula: see text] that determine the SCG in Jordan superalgebras. We use these to calculate the SCG for the Jordan superalgebra [Formula: see text], [Formula: see text]. Finally, we prove that [Formula: see text], [Formula: see text]. |
| Databáze: | OpenAIRE |
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