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.

Obstruction theory in action accessible categories / A.S. Cigoli, G. Metere, A. Montoli. - In: JOURNAL OF ALGEBRA. - ISSN 0021-8693. - 385:(2013 Jul 01), pp. 27-46. [10.1016/j.jalgebra.2013.03.020]

Obstruction theory in action accessible categories

A.S. Cigoli
Primo
;
G. Metere;A. Montoli
2013

Abstract

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.
obstruction theory; action accessible categories; Leibniz algebras
Settore MAT/02 - Algebra
1-lug-2013
Article (author)
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/221911
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