Related papers: Polymorphism of Representations of Universal Algeb…

Theory of representations of universal algebra is a natural development of the theory of universal algebra. In the book, I considered representation of universal algebra, diagram of representations and examples of representation. Morphism…

Theory of representations of universal algebra is a natural development of the theory of universal algebra. Morphism of the representation is the map that conserve the structure of the representation. Exploring of morphisms of the…

We say that there is a representation of the universal algebra B in the universal algebra A if the set of endomorphisms of the universal algebra A has the structure of universal algebra B. Therefore, the role of representation of the…

The concept of a crossed tensor product of algebras is studied from a few points of views. Some related constructions are considered. Crossed enveloping algebras and their representations are discussed. Applications to the noncommutative…

We introduce a nonsymmetric, associative tensor product among representations of Cuntz algebras by using embeddings. We show the decomposition formulae of tensor products for permutative representations explicitly We apply decomposition…

In this paper, we complete the classification of representation-finite tensor product algebras in terms of quiver with relations.

We construct the tensor product for f-algebras, including proving a universal property for it, and investigate how it preserves algebraic properties of the factors.

We prove a theorem about the derivation algebra of the tensor product of two algebras. As an application, we determine the derivation algebra of the fixed point algebra of the tensor product of two algebras, with respect to the tensor…

The classification of the representations of the generalized deformed oscillator algebra is given together with several comments about possibility of introducing a coproduct structure in some type of deformed oscillator algebra.

We consider the tensor product of modules over the polynomial algebra corresponding to the usual tensor product of linear operators. We present a general description of the representation ring in case the ground field k is perfect. It is…

We consider general linear superalgebra (type A) and tensor with Laurent polynomial ring in several variables. We then consider the universal central extension of this Lie superalgebra which we call toroidal superalgebra. We give a faithful…

Several structural properties of a universal algebra can be seen from the higher commutators of its congruences. Even on a finite algebra, the sequence of higher commutator operations is an infinite object. In the present paper, we exhibit…

The goal of this paper is to consider some relations between varieties of representations of groups and varieties of associative algebras. The main emphasis is put on the varieties of representations of groups induced by the varieties of…

We give a conceptual explanation of universal deformation formulas for unital associative algebras and prove some results on the structure of their moduli spaces. We then generalize universal deformation formulas to other types of algebras…

This note aims to investigate the tensor product of two given Hilbert quasi *-algebras and its properties. The construction proposed in this note turns out to be again a Hilbert quasi *-algebra, thus interesting representability properties…

Module is effective representation of ring in Abelian group. Linear map of module over commutative ring is morphism of corresponding representation. This definition is the main subject of the book. To consider this definition from more…

In the paper I considered algebra of polynomials over associative D-algebra with unit. Using the tensor notation allows to simplify the representation of polynomial. I considered questions related to divisibility of polynomial of any power…

Primarily this paper presents an expository report on alternatives to the traditional methods of classifying representations of finite dimensional algebras. Some new results illustrating such alternatives for algebras with only finitely…

This is an expository paper on tensor products where the standard approaches for constructing concrete instances of algebraic tensor products of linear spaces, via quotient spaces or via linear maps of bilinear maps, are reviewed by…

In this short note, we give a new sufficient condition for a linear map from a product of copies of a field to endomorphisms of a finite dimensional vector space over the same field to be an algebra homomorphism. We expect that this result…