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arXiv · 2501.01562

Hook Theorem for Superalgebras with Superinvolution or Graded Involution

Irina Sviridova·Renata A. Silva
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Abstract

We consider a superalgebra with a superinvolution or graded involution $\#$ over a field $F$ of characteristic zero and assume that it is a $PI$-algebra. In this paper, we present the proof of a version of the celebrated hook theorem \cite{SAR} for the case of multilinear $\#$-superidentities. This theorem provides important combinatorial characteristics of identities in the language of symmetric group representations. Furthermore, we present an analogue of Amitsur identities for $\#$-superalgebras, which are polynomial interpretations of the mentioned combinatorial characteristics, as a consequence of the hook theorem.

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Irina Sviridova, Renata A. Silva. 2025-01-02. Hook Theorem for Superalgebras with Superinvolution or Graded Involution. https://arxiv.org/abs/2501.01562

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