H-Unitality of Smooth Groupoid Algebras

TL;DR

This paper proves that certain smooth groupoid algebras are H-unital, enabling excision in Hochschild and cyclic homology, and extends previous results like the Dixmier-Malliavin theorem in this context.

Contribution

It establishes H-unitality for smooth groupoid algebras and related ideals, extending the understanding of their homological properties.

Findings

H-unitality of convolution algebras on Lie groupoids

H-unitality of ideals associated with invariant subsets

Excision properties in Hochschild and cyclic homology

Abstract

We show that the convolution algebra of smooth, compactly-supported functions on a Lie groupoid is H-unital in the sense of Wodzicki. We also prove H-unitality of infinite order vanishing ideals associated to invariant, closed subsets of the unit space. This furthermore gives H-unitality for the quotients by such ideals, which are noncommutative algebras of Whitney functions. These results lead immediately to excision properties in discrete Hochschild and cyclic homology around invariant, closed subsets. This work extends previous work of the author establishing the Dixmier-Malliavin theorem in this setting.