Homology Operations in Symmetric Homology

Details Homology Operations in Symmetric Homology Homology Operations in Symmetric Homology

2009-04-06

arxiv.org/abs/0904.1023v1

Mathematics

Algebraic Topology

19 pages

Scientific paper

Symmetric homology of a unital algebra $A$ over a commutative ground ring $k$ has been defined using derived functors and the symmetric bar construction of Fiedorowicz, in an analogous way as cyclic, dihedral or quaternionic homology has been defined. In this paper, it is found that the $HS_*(A)$ admits Dyer-Lashoff homology operations, and indeed, there is a Pontryagin product structure making $HS_*(A)$ into an associative commutative graded algebra. Some explicit computations are shown in low degree.

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