On Regular Quantum Commutative Algebras
Fuente:
arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866914531091939328 |
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| author | Bahturin, Yuri Centrone, Lucio Pereira, Kauê |
| author_facet | Bahturin, Yuri Centrone, Lucio Pereira, Kauê |
| contents | Let $K$ be an algebraically closed field of characteristic different from $2$. We provide a positive solution to the Bahturin--Regev conjecture in the general finite-dimensional (non-graded) setting, assuming that $\operatorname{char}(K)$ does not divide the quantum length of a minimal regular quantum commutative decomposition. Furthermore, we obtain a criterion, formulated in terms of regular quantum commutative decompositions, under which a set-grading on a semisimple associative algebra is realized as a group grading. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_03688 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On Regular Quantum Commutative Algebras Bahturin, Yuri Centrone, Lucio Pereira, Kauê Rings and Algebras 16R10, 16R50, 16W55, 16T05 Let $K$ be an algebraically closed field of characteristic different from $2$. We provide a positive solution to the Bahturin--Regev conjecture in the general finite-dimensional (non-graded) setting, assuming that $\operatorname{char}(K)$ does not divide the quantum length of a minimal regular quantum commutative decomposition. Furthermore, we obtain a criterion, formulated in terms of regular quantum commutative decompositions, under which a set-grading on a semisimple associative algebra is realized as a group grading. |
| title | On Regular Quantum Commutative Algebras |
| topic | Rings and Algebras 16R10, 16R50, 16W55, 16T05 |
| url | https://arxiv.org/abs/2605.03688 |