Abstract
We determine minimal Cayley–Hamilton and Capelli identities for matrices over a Grassmann algebra of finite rank. For minimal standard identities, we give lower and upper bounds on the degree. These results improve on upper bounds given by L. Márki, J. Meyer, J. Szigeti and L. van Wyk in a recent paper.
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Research partially supported by MTA Rényi Lendület “Groups and Graphs” research group, by ERC Consolidator Grant 648017 and by Hungarian National Foundation for Scientific Research (OTKA), grants no. K109684 and K104206.
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Frenkel, P.E. Polynomial identities for matrices over the Grassmann algebra. Isr. J. Math. 220, 791–801 (2017). https://doi.org/10.1007/s11856-017-1533-8
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DOI: https://doi.org/10.1007/s11856-017-1533-8