We prove that all semisimple varieties of FLew-algebras are discriminator varieties. A characterisation of discriminator and EDPC varieties of FLew-algebras follows. It matches exactly a natural classification of logics over FLew proposed by H. Ono.

This dissertation studies some matrix results and gives their generalizations in the context of semisimple Lie groups. The adjoint orbit is the primary object in our study. The dissertation consists of four chapters. Chapter 1 is a brief introduction about the interplay between matrix theory and Lie theory. In Chapter 2 we introduce some structure theory of semisimple Lie groups and Lie algebra...

We find the normal form of nilpotent elements in semisimple Lie algebras that generalizes Jordan slN, using theory cyclic elements.

The fundamental ideas of the definition of solvable and semisimple Bol algebras are given and some related theorems.

A new class of associative algebras is introduced and studied. These algebras are related to simple complex Lie algebras (or root systems). Roughly speaking, they are finite dimensional approximations to the enveloping algebra U(g) viewed as a module over its center. It seems that several important questions on semisimple algebras and their representations can be formulated, studied and sometim...

We consider the class of complex Lie algebras for which the Koszul 3-form is zero, and prove that it contains all quotients of Borel subalgebras, or of their nilradicals, of finite dimensional complex semisimple Lie algebras. A list of Kac-Moody types for indecomposable nilpotent complex Lie algebras of dimension ≤ 7 is given.

This note is to study a variety of graded algebras that arise from the induced representations for semisimple algebraic groups and quantum groups. These algebras will play an important role in a study of the cohomology groups of line bundles over the flag varieties. This short note concentrates on the calculation of the Gelfand-Kirillov dimensions of these algebras.

In this paper, we will study some connections between Hilbert algebras and binary block-codes.With these codes, we can eassy obtain orders which determine suplimentary properties on these algebras. We will try to emphasize how, using binary block-codes, we can provide examples of classes of Hilbert algebras with some properties, in our case, classes of semisimple Hilbert algebras and classes of...