Embedding of Jordan Superalgebras into the Superalgebras of Jordan Brackets

Сибирский математический журнал

article

V. N. Zhelyabin¹ 

[1] Sobolev Institute of Mathematics

关键词: associative commutative superalgebra;    Jordan superalgebra;    differential algebra;    Grassmann algebra;    superalgebra of a bilinear form;    derivation;    composition algebra;    superalgebra of a Jordan bracket;    bracket of vector type;    Poisson bracket;    Kantor double;   

DOI  :  10.1134/S003744662001005X

学科分类：数学（综合）

来源: Izdatel stvo Instituta Matematiki Rossiiskoi Akademii Nauk

【 摘 要 】

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.

【 授权许可】

CC BY