×

Symmetric continuous cohomology of topological groups. (English) Zbl 1275.22010

In 2009, M. D. Staic introduced a symmetric cohomology of abstract groups (see [J. Algebra 322, No. 4, 1360–1378 (2009; Zbl 1172.81014)]). The author introduces a continuous variant of Staic’s construction, enabling him to give a characterization of topological group extensions which correspond to elements of the second symmetric continuous cohomology. Another important result is derived for profinite groups with coefficients in a discrete module. It turns out that the symmetric continuous cohomology of such groups is the direct limit of the symmetric cohomology of finite groups. At the end of the paper, the results are carried over to Lie groups, where a smooth version of the symmetric cohomology groups is being defined.

MSC:

22E41 Continuous cohomology of Lie groups
54H11 Topological groups (topological aspects)
57T10 Homology and cohomology of Lie groups
20J06 Cohomology of groups

Citations:

Zbl 1172.81014
PDFBibTeX XMLCite
Full Text: DOI arXiv