arXiv:0708.1575 Abstract | arXiv Analytics

arXiv:0708.1575 [math.AT]Abstract References Reviews Resources

Symmetric Homology of Algebras

Published 2007-08-11, updated 2007-11-05Version 4

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.

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

Categories: math.AT

Subjects: 16E40, 55P45, 55S12

Keywords: cyclic homology, crossed simplicial groups, general development, computing symmetric homology, cyclic groups

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