For every semi-simple Lie algebra g one can construct the DrinfeldJimbo algebra U h (g). This algebra is a deformation Hopf algebra defined by generators and relations. To study the representation theory of U h (g), Drinfeld used the KZ-equations to construct a quasi-Hopf algebra Ag . He proved that particular categories of modules over the algebras U h (g) and Ag are tensor equivalent. Analogo...

• Vectorspaces over division rings • Matrices, opposite rings • Semi-simple modules and rings • Semi-simple algebras • Reduced trace and norm • Other criteria for simplicity • Involutions • Brauer group of a field • Tensor products of fields • Crossed product construction of simple algebras • Cyclic algebra construction of simple algebras • Quaternion algebras • Examples • Unramified extensions...

The notion of semi-BCI algebras is introduced and some of its properties are investigated. This algebra is another generalization for BCI-algebras. It arises from the “intervalization” of BCI algebras. Semi-BCI have a similar structure to Pseudo-BCI algebras however they are not the same. In this paper we also provide an investigation on the similarity between these classes of algebras by showi...

We present a category equivalent to that of semi-Nelson algebras. The objects in this are pairs consisting semi-Heyting algebra and one its filters. filters must contain all the dense elements satisfy an additional technical condition. also show case dually hemimorphic algebras, not necessary is

Pseudo-Galois extensions are shown to be depth two extensions. Studying its left bialgebroid, we construct an enveloping Hopf algebroid for the semi-direct product of groups or involutive Hopf algebras and their module algebras. It is a type of cofibered sum of two inclusions of the Hopf algebra into the semi-direct product and its derived right crossed product. Van Oystaeyen and Panaite observ...

We demonstrate that the notions of derivative representation of a Lie algebra on a vector bundle, of semi-linear representation of a Lie group on a vector bundle, and related concepts, may be understood in terms of representations of Lie algebroids and Lie groupoids, and we indicate how these notions extend to derivative representations of Lie algebroids and semi-linear representations of Lie g...

This paper introduces an imperative process algebra based on ACP (Algebra of Communicating Processes). Like other algebras, this deals with processes the kind that arises from execution programs. It distinguishes itself already existing algebras among things by supporting abstraction actions are considered not to be visible. The support opens interesting application possibilities algebra. goes ...