Crossed modules and symmetric cohomology of groups

Abstract

This paper links the third symmetric cohomology (introduced by Staic [9] and Zarelua [11]) to crossed modules with certain properties. The equivalent result in the language of 2-groups states that an extension of 2groups corresponds to an element of HS 3 iff it possesses a section which preserves inverses in the 2-categorical sense. This ties in with Staic's (and Zarelua's) result regarding HS 2 and abelian extensions of groups.

Symmetric Hochschild cohomology of twisted group algebras

“…There is a growing interest in the study of symmetric cohomology in the last years. We mention [6], where Pirashvili investigates the relation with the so-called exterior cohomology; we also mention [1] and [7].…”