6533b839fe1ef96bd12a65ee

RESEARCH PRODUCT

Obstruction theory in action accessible categories

Giuseppe MetereAndrea MontoliAlan S. Cigoli

subject

Algebra and Number TheoryGroup (mathematics)Accessible categoryAction accessible categorieObstruction theoryMathematics::Algebraic TopologyAction accessible categoriesCohomologyAction (physics)Action accessible categories; Leibniz algebras; Obstruction theoryLeibniz algebraAlgebraSettore MAT/02 - AlgebraMathematics::K-Theory and HomologyMathematics::Category TheoryLie algebraObstruction theoryLeibniz algebrasAssociative propertyObstruction theorymatMathematics

description

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.

yearjournalcountryeditionlanguage
2013-07-01
10.1016/j.jalgebra.2013.03.020https://hdl.handle.net/2078.1/183197