Actors in categories of interest

Abstract

For an object $A$ of a category of interest $\mathbb{C}$ we construct the group with operations $\mathfrak{B}(A)$ and the semidirect product $\mathfrak{B}(A)⋉A$ and prove that there exists an actor of $A$ in $\mathbb{C}$ if and only if $\mathfrak{B}(A)⋉A\in \mathbb{C}$. The cases of groups, Lie, Leibniz, associative, commutative associative, alternative algebras, crossed and precrossed modules are considered. The paper contains some results for the case ${\Omega }_2=\{+,\ast ,{\ast }^{\circ }\}$.

31 pages

Cited by in corpus (1)

• Actor of an alternative algebra