Generators for Decompositions of Tensor Products of Indecomposable Modules

Michael J. J. Barry

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arXiv · 2201.03475

Generators for Decompositions of Tensor Products of Indecomposable Modules

Michael J. J. Barry

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Abstract

Let $F$ be a field of non-zero characteristic $p$, let $G$ be a cyclic group of order $q =p^a$ for some positive integer $a$, and let $U$ and $W$ be indecomposable $F G$-modules. We identify a generator for each of the indecomposable components of $U \otimes W$ in terms of a particular $F$-basis of $U \otimes W$, extending previous work in which each component occurred with multiplicity one. An anonymous reviewer helped us realize that our results are really just a translation of previous results of Iiwa and Iwamatsu to our situation.

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BibTeX RIS

Michael J. J. Barry. 2022-01-10. Generators for Decompositions of Tensor Products of Indecomposable Modules. https://arxiv.org/abs/2201.03475

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