On the cyclic homology of supermatrices

TL;DR

This paper demonstrates that the generalized supertrace induces an isomorphism between the cyclic homologies of a superalgebra and its supermatrix algebra, extending known Hochschild homology results.

Contribution

It establishes that the supertrace map also induces an isomorphism between the cyclic homologies of superalgebras and their supermatrix counterparts.

Findings

Supertrace induces isomorphism between cyclic homologies

Extension of Hochschild homology results to cyclic homology

Provides a new tool for studying superalgebra structures

Abstract

The aim of this note is to show that the generalized supertrace, constructed in another paper of the author, inducing an isomorphism between the Hochschild homology of a superalgebra and that of the superalgebra of square supermatrices of a given type over $A$, induces, also, an isomorphism between the cyclic homologies of the two superalgebras.