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arXiv · 1901.07085

The Minimal Degree Standard Identity on $M_nE^2$ and $M_nE^3$

Barbara Anna Balázs·Szabolcs Mészáros
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Abstract

We prove an Amitsur--Levitzki-type theorem for Grassmann algebras, stating that the minimal degree of a standard identity that is a polynomial identity of the ring of $n \times n$ matrices over the $m$-generated Grassmann algebra is at least $2\left\lfloor\frac{m}{2}\right\rfloor+4n-4$ for all $n,m\geq 2$ and this bound is sharp for $m=2,3$ and any $n\geq 2$. The arguments are purely combinatorial, based on computing sums of signs corresponding to Eulerian trails in directed graphs.

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Barbara Anna Balázs, Szabolcs Mészáros. 2019-02-27. The Minimal Degree Standard Identity on $M_nE^2$ and $M_nE^3$. https://arxiv.org/abs/1901.07085

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