On Commutative Tensor Factors of Group Algebras

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2026_algebras_garcia_commutative.pdf (263.03 KB)
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URI: https://hdl.handle.net/10347/46770
ISSN: 1386-923X
E-ISSN: 1572-9079
DOI: 10.1007/s10468-026-10379-4

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2026-02-06

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Springer
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Abstract

We prove that any tensor product factorization with a commutative tensor factor of a modular group algebra over a prime field comes from a direct product decomposition of the group basis. This extends previous work by Carlson and Kovács for the commutative case and answers one of their questions in certain cases.

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Group algebras| Tensor factors| Positive characteristic

Bibliographic citation

García-Lucas, D., Río, Á. del, & Sakurai, T. (2026) On Commutative Tensor Factors of Group Algebras. Algebras and Representation Theory, 29, 153–160. https://doi.org/10.1007/s10468-026-10379-4

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Open Access funding provided thanks to the CRUE-CSIC agreement with Springer Nature. The first two authors have been partially supported by Grant PID2020-113206GB-I00 funded by MCIN/AEI/10.13039/501100011033 and by Grant Fundación Séneca 22004/PI/22.

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© TheAuthor(s) 2026. This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
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