Geodesic
Basis of Graded Identities of the Superalgebra $M_{1,2}(F)$
Matematičeskie zametki, Tome 85 (2009) no. 4, pp. 483-501.

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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.
Mots-clés : matrix algebra, permutation group, Young tableau
Keywords: superalgebra, Grassmann envelope, graded algebra, graded identity, ideal. 
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I. V. Averyanov. Basis of Graded Identities of the Superalgebra $M_{1,2}(F)$. Matematičeskie zametki, Tome 85 (2009) no. 4, pp. 483-501. http://geodesic.mathdoc.fr/item/MZM_2009_85_4_a0/

[1] O. M. Di Vincenzo, “On the graded identities of $M_{1,1}(E)$”, Israel J. Math., 80:3 (1992), 323–335 | DOI | MR | Zbl

[2] P. Koshlukov, S. S. Azevedo, “A basis for the graded identities of the matrix algebra of order two over a finite field of characteristic $p\ne2$”, Finite Fields Appl., 8:4 (2002), 597–609 | DOI | MR | Zbl

[3] S. Yu. Vasilovsky, “$\mathbf Z_n$-graded polynomial identities of the full matrix algebra of order $n$”, Proc. Amer. Math. Soc., 127:12 (1999), 3517–3524 | DOI | MR | Zbl

[4] S. S. Azevedo, “Graded identities for the matrix algebra of order $n$ over an infinite field”, Comm. Algebra, 30:12 (2002), 5849–5860 | DOI | MR | Zbl

[5] Y. Bahturin, V. Drensky, “Graded polynomial identities of matrices”, Linear Algebra Appl., 357:1 (2002), 15–34 | DOI | MR | Zbl

[6] G. Dzheims, Teoriya predstavlenii simmetricheskikh grupp, Matematika. Novoe v zarubezhnoi nauke, 32, Mir, M., 1982 | MR | Zbl

[7] Yu. P. Razmyslov, “Tozhdestva so sledom polnykh matrichnykh algebr nad polem kharakteristiki nul”, Izv. AN SSSR. Ser. matem., 38:4 (1974), 723–756 | MR | Zbl

[8] V. Drenski, “Minimalnyi bazis tozhdestv agebry matrits vtorogo poryadka nad polem kharakteristiki 0”, Algebra i logika, 20:3 (1981), 282–290 | MR | Zbl

[9] A. R. Kemer, Ideals of Identities of Associative Algebras, Transl. Math. Monogr., 87, Amer. Math. Soc., Providence, RI, 1991 | MR | Zbl