Generators for decompositions of tensor products of modules associated with standard Jordan partitions

DOI10.1080/00927872.2016.1226863zbMath1369.20008arXiv1508.01768OpenAlexW2964224857MaRDI QIDQ2985006

Michael J. J. Barry

Publication date: 12 May 2017

Published in: Communications in Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1508.01768

zbMATH Keywords

cyclic grouptensor productindecomposable modulemodule generator

Mathematics Subject Classification ID

Modular representations and characters (20C20) Group rings of finite groups and their modules (group-theoretic aspects) (20C05)

Cites Work

• Generators for decompositions of tensor products of modules.
• Decomposing modular tensor products: `Jordan partitions', their parts and \(p\)-parts
• Decomposing modular tensor products, and periodicity of `Jordan partitions'
• The decomposition of products in the modular representation ring of a cyclic group of prime power order
• Elementary divisors of tensor products and \(p\)-ranks of binomial matrices.
• Groups with a T. I. cyclic Sylow subgroup
• A canonical basis for the matrix transformation \(X \to AX+XB\)
• A canonical basis for the matrix transformation \(X\to AXB\)
• Decomposing tensor products and exterior and symmetric squares
• On a Question of Glasby, Praeger, and Xia
• On Jordan bases for the tensor product and Kronecker sum and their elementary divisors over fields of prime characteristic
• On the jordan form of the tensor product over fields of prime characteristic

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