Multipliers, $W$-algebras and the growth of generalized polynomial identities
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866917448920334336 |
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| author | Martino, Fabrizio Rizzo, Carla |
| author_facet | Martino, Fabrizio Rizzo, Carla |
| contents | Let $A$ be a $W$-algebra over a field $F$ of characteristic zero, where $W$ is any $F$-algebra. We first develop a comprehensive theory of generalized identities independent of the algebraic structure of $W$, using the multiplier algebra of $A.$ Then, we investigate the generalized variety generated by the $k\times k$ matrix algebra with a suitable action, proving that it exhibits almost polynomial growth of the generalized codimensions. Furthermore, we characterize the generalized varieties of almost polynomial growth generated by finite dimensional $W$-algebras. Finally, we provide a counterexample to the Specht property of generalized $T_W$-ideals in characteristic zero. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_12830 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Multipliers, $W$-algebras and the growth of generalized polynomial identities Martino, Fabrizio Rizzo, Carla Rings and Algebras Primary 16R10, 16R50, Secondary 16P90, 16G30 Let $A$ be a $W$-algebra over a field $F$ of characteristic zero, where $W$ is any $F$-algebra. We first develop a comprehensive theory of generalized identities independent of the algebraic structure of $W$, using the multiplier algebra of $A.$ Then, we investigate the generalized variety generated by the $k\times k$ matrix algebra with a suitable action, proving that it exhibits almost polynomial growth of the generalized codimensions. Furthermore, we characterize the generalized varieties of almost polynomial growth generated by finite dimensional $W$-algebras. Finally, we provide a counterexample to the Specht property of generalized $T_W$-ideals in characteristic zero. |
| title | Multipliers, $W$-algebras and the growth of generalized polynomial identities |
| topic | Rings and Algebras Primary 16R10, 16R50, Secondary 16P90, 16G30 |
| url | https://arxiv.org/abs/2502.12830 |