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This article is cited in 8 scientific papers (total in 8 papers)
Basis of Graded Identities of the Superalgebra $M_{1,2}(F)$
I. V. Averyanov Ulyanovsk State University
Abstract:
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.
Keywords:
matrix algebra, superalgebra, Grassmann envelope, graded algebra, graded identity, permutation group, Young tableau, ideal.
Received: 02.11.2007 Revised: 23.05.2008
Citation:
I. V. Averyanov, “Basis of Graded Identities of the Superalgebra $M_{1,2}(F)$”, Mat. Zametki, 85:4 (2009), 483–501; Math. Notes, 85:4 (2009), 467–483
Linking options:
https://www.mathnet.ru/eng/mzm4298https://doi.org/10.4213/mzm4298 https://www.mathnet.ru/eng/mzm/v85/i4/p483
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