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Hochschild homology of twisted crossed products and twisted graded Hecke algebras

Maarten Solleveld

Vol. 8 (2023), No. 1, 81–126
Abstract

Let A be a -algebra with an action of a finite group G, and consider a twisted crossed product A [G,]. We find the Hochschild homology of A [G,] for two classes of algebras A: rings of regular functions on nonsingular affine varieties, and graded Hecke algebras. The results are achieved via algebraic families of (virtual) representations and include a description of the Hochschild homology as a module over the centre of A [G,]. In noncommutative geometric terms, our results describe the differential forms on the space of irreducible representations of A [G,]. This paper prepares for a computation of the Hochschild homology of the Hecke algebra of a reductive p-adic group.

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Keywords
Hochschild homology, graded Hecke algebras, crossed products
Mathematical Subject Classification
Primary: 16E40
Secondary: 16S35, 20C08
Milestones
Received: 15 March 2022
Revised: 26 October 2022
Accepted: 1 December 2022
Published: 1 May 2023
Authors
Maarten Solleveld
IMAPP
Radboud Universiteit Nijmegen
Nijmegen
Netherlands