Specht property for the $2$-graded identities of $B_m$

Diogo Diniz; Manuela da Silva Souza

Specht property for the $2$-graded identities of $B_m$

Rings and Algebras 2016-01-14 v1

Authors: Diogo Diniz , Manuela da Silva Souza

Abstract

Let $K$ be a field of characteristic zero and $V$ a vector space of dimension $m>1$ with a nondegenerate symmetric bilinear form $f:V\times V \rightarrow K$ . The Jordan algebra $B_m=K\oplus V$ of the form $f$ is a superalgebra with this decomposition. We prove that the ideal of all the $2$ -graded identities of $B_m$ satisfies the Specht property and we compute the $2$ -graded cocharacter sequence of $B_m$ .

Keywords

Specht property graded identity Jordan algebra superalgebra bilinear form cocharacter sequence field of characteristic zero

Cite

@article{arxiv.1601.03351,
  title  = {Specht property for the $2$-graded identities of $B_m$},
  author = {Diogo Diniz and Manuela da Silva Souza},
  journal= {arXiv preprint arXiv:1601.03351},
  year   = {2016}
}

Comments

10 pages

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