Symmetric continuous cohomology of topological groups

Abstract

In this paper, we introduce a symmetric continuous cohomology of topological groups. This is obtained by topologizing a recent construction due to Staic (J. Algebra 322 (2009), 1360-1378), where a symmetric cohomology of abstract groups is constructed. We give a characterization of topological group extensions that correspond to elements of the second symmetric continuous cohomology. We also show that the symmetric continuous cohomology of a profinite group with coefficients in a discrete module is equal to the direct limit of the symmetric cohomology of finite groups. In the end, we also define symmetric smooth cohomology of Lie groups and prove similar results.

arXiv comment23 pages, to appear in Homology Homotopy and Applications

Cited by in corpus (2)

• Exterior and symmetric (co)homology of groups
• Symmetric cohomology and symmetric Hochschild cohomology of cocommutative Hopf algebras