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Matematicheskie Zametki, 2009, Volume 85, Issue 4, Pages 483–501
DOI: https://doi.org/10.4213/mzm4298
(Mi mzm4298)
 

This article is cited in 8 scientific papers (total in 8 papers)

Basis of Graded Identities of the Superalgebra M1,2(F)M1,2(F)

I. V. Averyanov

Ulyanovsk State University
Full-text PDF (506 kB) Citations (8)
References:
Abstract: Denote by Matk,l(F)Matk,l(F) the algebra Mn(F)Mn(F) of matrices of order n=k+ln=k+l with the grading (Mat0k,l(F),Mat1k,l(F))(Mat0k,l(F),Mat1k,l(F)), where Mat0k,l(F)Mat0k,l(F) admits the basis {eij,ik,jk}{eij,i>k,j>k} and Mat1k,l(F) admits the basis {eij,ik,j>k}{eij,i>k,jk}. Denote by Mk,l(F) the Grassmann envelope of the superalgebra Matk,l(F). In the paper, bases of the graded identities of the superalgebras Mat1,2(F) and M1,2(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
English version:
Mathematical Notes, 2009, Volume 85, Issue 4, Pages 467–483
DOI: https://doi.org/10.1134/S0001434609030195
Bibliographic databases:
UDC: 512.552
Language: Russian
Citation: I. V. Averyanov, “Basis of Graded Identities of the Superalgebra M1,2(F)”, Mat. Zametki, 85:4 (2009), 483–501; Math. Notes, 85:4 (2009), 467–483
Citation in format AMSBIB
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  • This publication is cited in the following 8 articles:
    1. S. Yu. Antonov, A. V. Antonova, “O kvazimnogochlenakh Kapelli. III”, Izv. Sarat. un-ta. Nov. ser. Ser.: Matematika. Mekhanika. Informatika, 21:2 (2021), 142–150  mathnet  crossref  elib
    2. S. Yu. Antonov, A. V. Antonova, “O kvazimnogochlenakh Kapelli. II”, Izv. Sarat. un-ta. Nov. ser. Ser.: Matematika. Mekhanika. Informatika, 20:1 (2020), 4–16  mathnet  crossref
    3. 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
    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. Aque S., Giambruno A., “Cocharacters of Bilinear Mappings and Graded Matrices”, Algebr. Represent. Theory, 16:6 (2013), 1621–1646  crossref  mathscinet  zmath  isi  scopus
    6. 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
    7. 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
    8. V. P. Maslov, “A new distribution generalizing the Bose–Einstein distribution”, Theoret. and Math. Phys., 159:2 (2009), 684–685  mathnet  mathnet  crossref  crossref  isi  scopus
    Citing articles in Google Scholar: Russian citations, English citations
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