Trace theories and localization

TL;DR

This paper generalizes Hochschild homology by incorporating non-additive trace functors, demonstrating that many classical properties, including Keller's Localization Theorem, still hold in this broader context.

Contribution

It introduces a novel approach to Hochschild homology using trace functors, extending its properties and localization results to non-additive settings.

Findings

Many properties of Hochschild homology are preserved under the new generalization.

Keller's Localization Theorem remains valid in the generalized framework.

The approach broadens the applicability of Hochschild homology in algebraic contexts.

Abstract

We show how one can twist the definition of Hochschild homology of an algebra or a DG algebra by inserting a possibly non-additive trace functor. We then prove that many of the usual properties of Hochschild homology survive such a generalization. In some cases this even includes Keller's Localization Theorem.