Сибирский математический журнал | |
The Superalgebras of Jordan Brackets Defined by the \( n \) -Dimensional Sphere | |
article | |
V. N. Zhelyabin1  A. S. Zakharov2  | |
[1] Sobolev Institute of Mathematics;Novosibirsk State University;Novosibirsk State Technical University | |
关键词: associative commutative superalgebra; Jordan superalgebra; differential algebra; Grassmann algebra; superalgebra of a bilinear form; polynomial algebra; derivation; Jordan bracket; bracket of vector type; Poisson bracket; projective module; affine space; sphere; | |
DOI : 10.1134/S0037446620040072 | |
学科分类:数学(综合) | |
来源: Izdatel stvo Instituta Matematiki Rossiiskoi Akademii Nauk | |
【 摘 要 】
We study the generalized Leibniz brackets on the coordinate algebra of the $ n $ -dimensional sphere. In the case of the one-dimensional sphere, we show that each of these is a bracket of vector type. Each Jordan bracket on the coordinate algebra of the two-dimensional sphere is a generalized Poisson bracket. We equip the coordinate algebra of a sphere of odd dimension with a Jordan bracket whose Kantor double is a simple Jordan superalgebra. Using such superalgebras, we provide some examples of the simple abelian Jordan superalgebras whose odd part is a finitely generated projective module of rank 1 in an arbitrary number of generators. An analogous result holds for the Cartesian product of the sphere of even dimension and the affine line. In particular, in the case of the 2-dimensional sphere we obtain the exceptional Jordan superalgebra. The superalgebras we constructed give new examples of simple Jordan superalgebras.
【 授权许可】
CC BY
【 预 览 】
Files | Size | Format | View |
---|---|---|---|
RO202106300004644ZK.pdf | 220KB | download |