Symmetric Homology of Algebras

Details Symmetric Homology of Algebras Symmetric Homology of Algebras

2007-08-11

arxiv.org/abs/0708.1575v4

Mathematics

Algebraic Topology

14 pages, references and discussion of recent related work by Vrecica and Zivaljevic has been added

Scientific paper

In this note, we outline the general development of a theory of symmetric homology of algebras, an analog of cyclic homology where the cyclic groups are replaced by symmetric groups. This theory is developed using the framework of crossed simplicial groups and the homological algebra of module-valued functors. The symmetric homology of group algebras is related to stable homotopy theory. Two spectral sequences for computing symmetric homology are constructed. The relation to cyclic homology is discussed and some conjectures and questions towards further work are discussed.

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