On Regular Quantum Commutative Algebras

Fuente: arXiv
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Main Authors: Bahturin, Yuri, Centrone, Lucio, Pereira, Kauê
Format: Preprint
Published: 2026
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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