Specht property for the algebra of upper triangular matrices of size two with a Taft’s algebra action
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Bibliographic record
Abstract
Abstract Let F be a field of characteristic zero, and let $UT_2$ be the algebra of $2 \times 2$ upper triangular matrices over F . In a previous paper by Centrone and Yasumura, the authors give a description of the action of Taft’s algebras $H_m$ on $UT_2$ and its $H_m$ -identities. In this paper, we give a complete description of the space of multilinear $H_m$ -identities in the language of Young diagrams through the representation theory of the hyperoctahedral group. We finally prove that the variety of $H_m$ -module algebras generated by $UT_2$ has the Specht property, i.e., every $T^{H_m}$ -ideal containing the $H_m$ -identities of $UT_2$ is finitely based.
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| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.002 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.014 | 0.000 |
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