Bimultiplications and Annihilators of Crossed Modules in Associative Algebras

Abstract

In this paper, we present a generalization of the concept of the bimultiplication algebra by defining the bimultiplication of crossed modules in associative algebras. Using this structure, we construct the actor of a crossed module in associative algebras, and we obtain annihilators of crossed modules as the kernel of a crossed module morphism from a crossed module to its actor. Moreover, we construct a link between this morphism and a crossed square, two-dimensional crossed module.

Keywords

• Bimultiplication crossed module
• actor crossed module
• annihilator of crossed module
• crossed square

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