A Comparison Map for Symmetric Homology and Gamma Homology

TL;DR

This paper constructs a comparison map linking gamma homology and symmetric homology theories for augmented, commutative algebras over a unital commutative ring, clarifying their relationship.

Contribution

It introduces a comparison map between gamma homology and symmetric homology theories for a specific class of algebras, providing new insights into their connection.

Findings

Established a formal comparison map between the two homology theories.

Clarified the relationship between gamma homology and symmetric homology.

Enhanced understanding of homology theories for augmented, commutative algebras.

Abstract

We construct a comparison map between the gamma homology theory of Robinson and Whitehouse and the symmetric homology theory of Fiedorowicz and Ault in the case of an augmented, commutative algebra over a unital commutative ground ring.