Сибирский математический журнал | |
Embedding of Jordan Superalgebras into the Superalgebras of Jordan Brackets | |
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
【 预 览 】
Files | Size | Format | View |
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RO202106300004591ZK.pdf | 198KB | download |