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arXiv · 2201.11186

Hochschild homology of twisted crossed products and twisted graded Hecke algebras

Maarten Solleveld
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Abstract

Let A be a \C-algebra with an action of a finite group G, let $\natural$ be a 2-cocycle on $G$ and consider the twisted crossed product $A \rtimes \C [G,\natural]$. We determine the Hochschild homology of $A \rtimes \C [G,\natural]$ for two classes of algebras A: - rings of regular functions on nonsingular affine varieties, - graded Hecke algebras. The results are achieved via algebraic families of (virtual) representations and include a description of the Hochschild homology as module over the centre of $A \rtimes \C [G,\natural]$. This paper prepares for a computation of the Hochschild homology of the Hecke algebra of a reductive p-adic group.

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Maarten Solleveld. 2022-01-26. Hochschild homology of twisted crossed products and twisted graded Hecke algebras. https://doi.org/10.2140/akt.2023.8.81

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