We show that, in semi-abelian action accessible categories (such as the categories of groups, Lie algebras, rings, associative algebras and Poisson algebras), the obstruction to the existence of extensions is classified by the second cohomology group in the sense of Bourn. Moreover, we describe explicitly the obstruction to the existence of extensions in the case of Leibniz algebras, comparing Bourn cohomology with Loday-Pirashvili cohomology of Leibniz algebras.
|Numero di pagine||20|
|Rivista||Journal of Algebra|
|Stato di pubblicazione||Published - 2013|
All Science Journal Classification (ASJC) codes
- Algebra and Number Theory