The Dennis' Supertrace and the Hochschild Homology of Supermatrices

Abstract

We construct, in this paper, a generalization of the Dennis trace (for matrices) to the case of the supermatrices over an arbitrary (not necessarily commutative) superalgebra with unit. By analogy with the ungraded case, we show how it is possible to use this map to construct an isomorphism from the Hochschild homology of the superalgebra to the Hochschild homology of the supermatrix algebra.

arXiv comment13 pages. Russian Journal of Mathematical Physics, in press

References in corpus (2)

• On the Morita invariance of the Hochschild homology of superalgebras
• On the cyclic homology of supermatrices

Cited by in corpus (1)

• Universal central extensions of $\mathfrak{sl}(m,n,A)$ of small rank over associative superalgebras