Universal Strict General Actors and Actors in Categories of Interest

作者：Casas J M; Datuashvili T; Ladra M^*

来源：Applied Categorical Structures, 2010, 18(1): 85-114.

DOI：10.1007/s10485-008-9166-z

• Action
• Group with operations
• Associative algebra
• Lie algebra
• Leibniz algebra
• Alternative algebra
• Crossed module
• Category of interest
• Bimultipliers
• Biderivations

For any category of interest C we define a general category of groups with operations C(G), C -> C(G), and a universal strict general actor USGA(A) of an object A in C, which is an object of C(G). The notion of actor is equivalent to the one of split extension classifier defined for an object in more general settings of semi-abelian categories. It is proved that there exists an actor of A in C if and only if the semidirect product USGA(A) x A is an object of C, and if it is the case, then USGA(A) is an actor of A. We give a construction of a universal strict general actor for any A is an element of C, which helps to detect more properties of this object. The cases of groups, Lie, Leibniz, associative, commutative associative, alternative algebras, crossed and precrossed modules are considered. The examples of algebras are given, for which always exist actors.

• 出版日期2010-2