Basis of Graded Identities of the Superalgebra $M_{1,2}(F)$

I. V. Averyanov

Matematičeskie zametki, Tome 85 (2009) no. 4, pp. 483-501

Résumé

Denote by $\operatorname{Mat}_{k,l}(F)$ the algebra $M_n(F)$ of matrices of order $n=k+l$ with the grading $(\operatorname{Mat}^0_{k,l}(F), \operatorname{Mat}^1_{k,l}(F))$, where $\operatorname{Mat}^0_{k,l}(F)$ admits the basis $\{e_{ij},i\le k,j\le k\}\cup\{e_{ij},i>k,j>k\}$ and $\operatorname{Mat}^1_{k,l}(F)$ admits the basis $\{e_{ij},i\le k,j>k\}\cup\{e_{ij},i>k,j\ge k\}$. Denote by $M_{k,l}(F)$ the Grassmann envelope of the superalgebra $\operatorname{Mat}_{k,l}(F)$. In the paper, bases of the graded identities of the superalgebras $\operatorname{Mat}_{1,2}(F)$ and $M_{1,2}(F)$ are described.

Détail

Mots-clés : matrix algebra, permutation group, Young tableau
Keywords: superalgebra, Grassmann envelope, graded algebra, graded identity, ideal.