Abstract
We determine theS n ×S m -cocharacterX n,m of the algebraM 1,1(E) and prove that theT 2-ideal of its graded identities is generated by the polynomialsy 1 y 2−y 2 y 1 andz 1 z 2 z 3+z 3 z 2 z 1.
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References
A. Berele,Magnum P.I., Isr. J. Math.51 (1985), 13–19.
A. Berele,Cocharacters of Z/2Z-graded algebras, Isr. J. Math.61 (1988), 225–234.
G. D. James,The representation theory of the symmetric group, Lecture Notes in Mathematics628, Springer, Berlin, 1978.
A. R. Kemer,Varieties and Z 2-graded algebras, Math. USSR Izv.25 (1985), 359–374.
A. P. Popov,Identities of the tensor square of the Grassmann algebra, Algebra and Logic21 (1983), 293–316.
A. Regev,The polynomial identities of matrices in characteristic zero, Commun. Algebra8 (1980), 1417–1467.
A. Regev,On the identities of subalgebras of matrices over the Grassmann algebra, Isr. J. Math.58 (1987), 351–369.
A. Regev,Tensor product of matrix algebras over the Grassmann algebra, J. Algebra133 (1990), 351–369.
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Di Vincenzo, O.M. On the graded identities ofM 1,1(E). Israel J. Math. 80, 323–335 (1992). https://doi.org/10.1007/BF02808074
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DOI: https://doi.org/10.1007/BF02808074