On the Hochschild homology of l^1-rapid decay group algebras

TL;DR

This paper investigates the Hochschild homology of l^1-rapid decay group algebras for semi-hyperbolic groups, showing an injective decomposition into conjugacy classes, which advances understanding of their algebraic structure.

Contribution

It demonstrates the injectivity of the conjugacy class decomposition in Hochschild homology for a broad class of semi-hyperbolic groups, a novel result in this area.

Findings

Decomposition into conjugacy classes is injective for many semi-hyperbolic groups.

Provides new insights into the structure of Hochschild homology of rapid decay group algebras.

Enhances understanding of algebraic properties of semi-hyperbolic groups.

Abstract

We show that for many semi-hyperbolic groups the decomposition into conjugacy classes of the Hochschild homology of the l^1-rapid decay group algebra is injective.