On the representability of actions of Leibniz algebras and Poisson algebras

Abstract

In a recent paper, motivated by the study of central extensions of associative algebras, G. Janelidze introduces the notion of weakly action representable category. In this paper, we show that the category of Leibniz algebras is weakly action representable and we characterize the class of acting morphisms. Moreover, we study the representability of actions of the category of Poisson algebras by describing explicitly a universal strict general actor.

New version, revised following a corrigendum. Theorems 4.9 and 4.10 have been removed. Weak action representability of the category of commutative Poisson algebras remains an open problem

References in corpus (1)

• Central extensions of associative algebras and weakly action representable categories

Cited by in corpus (4)

• Weak representability of actions of non-associative algebras
• Action accessible and weakly action representable varieties of algebras
• Non-nilpotent Leibniz algebras with one-dimensional derived subalgebra
• On Lie-holomorphs of Leibniz algebras