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Embedding of Jordan Superalgebras into the Superalgebras of Jordan Brackets

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Abstract

We show that the Jordan bracket on an associative commutative superalgebra is extendable to the superalgebra of fractions. In particular, we prove that a unital simple abelian Jordan superalgebra is embedded into a simple superalgebra of a Jordan bracket. We also study the unital simple Jordan superalgebras whose even part is a field. We demonstrate that each of these superalgebras is either a superalgebra of a nondegenerate bilinear form, or a four-dimensional simple Jordan superalgebra, or a superalgebra of a Jordan bracket, or a superalgebra whose odd part is an irreducible module over a field.

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Authors and Affiliations

  1. Sobolev Institute of Mathematics, Novosibirsk, Russia

    V. N. Zhelyabin

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  1. V. N. Zhelyabin
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Correspondence to V. N. Zhelyabin.

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Russian Text © The Author(s), 2020, published in Sibirskii Matematicheskii Zhurnal, 2020, Vol. 61, No. 1, pp. 78–95.

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Zhelyabin, V.N. Embedding of Jordan Superalgebras into the Superalgebras of Jordan Brackets. Sib Math J 61, 62–75 (2020). https://doi.org/10.1134/S003744662001005X

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  • DOI: https://doi.org/10.1134/S003744662001005X

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