Wedderburn’s theorem on the structure of finite dimensional semisimple algebras is proved by using minimal prerequisites.

Representations of semisimple Lie algebras in the BGG category í µí²ª, by James E.

In this paper, we compute the Gram determinants associated to each cell module of the Birman-Wenzl algebras. As a by-product, we give the necessary and sufficient condition for semisimple Birman-Wenzl algebras over an arbitrary field.

The basic properties of multiplication algebras of nonassociative algebras over rings are introduced, including a discussion of multiplication algebras of tensor products of algebras. A characterization of semisimple artinian multiplication algebras is given along with a discussion of the nature of the simple factors of a multiplication algebra modulo its Jacobson radical. A criterion distingui...

We study some non-semisimple representations of affine Temperley–Lieb algebras and related cellular algebras. In particular, we classify extensions between simple standard modules. Moreover, we construct a completion which is an infinite dimensional cellular algebra.

The class of p-semisimple pseudo-BCI-algebras and the class of branchwise commutative pseudo-BCI-algebras are studied. It is proved that they form varieties. Some congruence properties of these varieties are displayed.

The category psBCI of pseudo-BCI-algebras and homomorphisms between them is investigated. It is also shown that the category psBCIp of p-semisimple pseudo-BCI-algebras and homomorphisms between them is a reflective subcategory of psBCI.

We propose a systematic procedure to construct polynomial algebras from intermediate Casimir invariants arising (semisimple or non-semisimple) Lie $\mathfrak{g}$. In this approach, we deal with explicit polynomials in the enveloping algebra of $\mathfrak{g} \oplus \mathfrak{g} \mathfrak{g}$. present examples show how these can display different behaviours and lead Abelian algebras, quadratic mo...

This work is an investigation into the structure and properties of Lie hypermatrix algebra generated by a semisimple basis. By using new algebraic tools; namely cubic hypermatrices I obtain an algebraic structure associated with the basis of a semisimple Lie algebra, and I show that the semisimple Lie basis is a generator of infinite periodic semisimple hypermatrix structures, that has a classi...

The category psBCI of pseudo-BCI-algebras and homomorphisms between them is investigated. It is also shown that the category psBCIp of p-semisimple pseudo-BCI-algebras and homomorphisms between them is a reflective subcategory of psBCI.