Hook Theorem for Superalgebras with Superinvolution or Graded Involution
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866915089219584000 |
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| author | Sviridova, Irina Silva, Renata A. |
| author_facet | Sviridova, Irina Silva, Renata A. |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2501_01562 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Hook Theorem for Superalgebras with Superinvolution or Graded Involution Sviridova, Irina Silva, Renata A. Rings and Algebras Representation Theory 16R10, 16R50, 16W50, 16W55, 16W10 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. |
| title | Hook Theorem for Superalgebras with Superinvolution or Graded Involution |
| topic | Rings and Algebras Representation Theory 16R10, 16R50, 16W50, 16W55, 16W10 |
| url | https://arxiv.org/abs/2501.01562 |