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Skew Hecke algebras

Lookup NU author(s): Dr James Waldron

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Abstract

© 2025 The Author(s). Published with license by Taylor & Francis Group, LLC. Let G be a finite group, (Formula presented.) a subgroup, R a commutative ring, A an R-algebra, and (Formula presented.) an action of G on A by R-algebra automorphisms. We study the associated skew Hecke algebra (Formula presented.) of H-invariant functions from (Formula presented.) to A, proving a number of common generalizations of results about skew group rings and about Hecke algebras of finite groups. We show that the construction is compatible with a number of group-theoretic and algebraic operations, and illustrate the main results for certain permutation actions on polynomial algebras.

Publication metadata

Author(s): Waldron J, Loveridge LD

Publication type: Article

Publication status: Published

Journal: Communications in Algebra

Year: 2025

Volume: 53

Issue: 11

Pages: 4624-4648

Online publication date: 30/04/2025

Acceptance date: 06/04/2025

Date deposited: 23/05/2025

ISSN (print): 0092-7872

ISSN (electronic): 1532-4125

Publisher: Taylor and Francis Ltd

URL: https://doi.org/10.1080/00927872.2025.2492345

DOI: 10.1080/00927872.2025.2492345

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