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Mat. Zametki, 2009, Volume 85, Issue 4, Pages 483–501 (Mi mz4298)  

This article is cited in 5 scientific papers (total in 5 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

DOI: https://doi.org/10.4213/mzm4298

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English version:
Mathematical Notes, 2009, 85:4, 467–483

Bibliographic databases:

UDC: 512.552
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

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. S. Yu. Antonov, “Some estimates for the least power of identities of subspaces $M_1^{(m,k)}(F)$ of the matrix superalgebra $M^{(m,k)}(F)$”, Russian Math. (Iz. VUZ), 56:5 (2012), 9–22  mathnet  crossref  mathscinet
    2. Aque S., Giambruno A., “Cocharacters of Bilinear Mappings and Graded Matrices”, Algebr. Represent. Theory, 16:6 (2013), 1621–1646  crossref  mathscinet  zmath  isi  scopus
    3. Aque S., “Computing the Z(2)-Cocharacter of 3 X 3 Matrices of Odd Degree”, Commun. Algebr., 41:4 (2013), 1405–1416  crossref  mathscinet  zmath  isi  elib  scopus
    4. S. Yu. Antonov, A. V. Antonova, “O kvazimnogochlenakh Kapelli”, Izv. Sarat. un-ta. Nov. ser. Ser. Matematika. Mekhanika. Informatika, 15:4 (2015), 371–382  mathnet  crossref  elib
    5. S. Yu. Antonov, A. V. Antonova, “K teoreme Chenga. III”, Izv. Sarat. un-ta. Nov. ser. Ser. Matematika. Mekhanika. Informatika, 18:2 (2018), 128–143  mathnet  crossref  elib
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