Periodic cyclic homology of Hecke algebras and their Schwartz completions

TL;DR

This paper demonstrates that the inclusion of an affine Hecke algebra into its Schwartz completion preserves periodic cyclic homology, establishing an isomorphism between these algebraic structures.

Contribution

It proves that the periodic cyclic homology remains unchanged under the Schwartz completion of affine Hecke algebras, a novel result in the field.

Findings

Inclusion induces isomorphism on periodic cyclic homology

Schwartz completion preserves cyclic homology

Advances understanding of algebraic invariants in representation theory

Abstract

We show that the inclusion of an affine Hecke algebra in its Schwartz completion induces an isomorphism on periodic cyclic homology.