Hook Theorem for Superalgebras with Superinvolution or Graded Involution

2025/01/02 by Sviridova, Irina, Silva, Renata A.
#16R10 #16R50 #16W10 #16W50 #16W55 #FOS: Mathematics #Representation Theory (math.RT) #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.2501.01562

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 \citeSAR 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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