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

A technique is developed to reduce the investigation of Nichols algebras of integrable Uq(g)-modules to the investigation of Nichols algebras of braided vector spaces with diagonal braiding. The results are applied to obtain information on the Gelfan’dKirillov dimension of these Nichols algebras and their defining relations if the braiding is of a special type and q is not a root of unity. For ...

Let U denote the half quantum group for a fixed simple Lie algebra. We examine some properties and representation of U. We prove that the Hopf algebra U is not quasi-cocommutative, and hence the category of left U-module is not a braided monoidal category. In the weight module category W , we describe all the simple objects and the projective objects. We also describe all simple Yetter-Drinfel’...