Related papers: Non-commutative first order differential calculus …

A free differential for an arbitrary associative algebra is defined as a differential with a uniqueness property. The existence problem for such a differential is posed. The notion of optimal calculi for given commutation rules is…

We give a Clifford correspondence for an algebra A over an algebraically closed field, that is an algorithm for constructing some finite-dimensional simple A-modules from simple modules for a subalgebra and endomorphism algebras. This…

We prove that if $B\subseteq A$ is an extension of finite dimensional algebras such that the projective dimension of $A/B$ as a $B$-bimodule is finite, if $A$ has finite finitistic dimension, then so does $B$. We exhibit examples…

We describe the representation theory of finitely generated indecomposable modules over artin algebras which do not lie on cycles of indecomposable modules involving homomorphisms from the infinite Jacobson radical of the module category.

In this paper, we classify the finite dimensional irreducible modules for affine BMW algebra over an algebraically closed field with arbitrary characteristic.

We propose a sheaf-theoretic approach to the theory of differential calculi on quantum principal bundles over non-affine bases. After recalling the affine case we define differential calculi on sheaves of comodule algebras as sheaves of…

Let $\Gamma$ be an $N^2$-dimensional bicovariant first order differential calculus on a Hopf algebra $SL_q(N)$. There are three possibilities to construct a differential Z-graded Hopf algebra $\Gamma^\wedge$ which contains $\Gamma$ as its…

Let $d$ be a positive integer. In a previous article we established a bijective correspondence between the following classes of objects, considered up to the appropriate notion of equivalence: differential graded algebras with…

We show how one can construct a differential calculus over an algebra where position variables x and momentum variables p have be defined. As the simplest example we consider the one-dimensional q-deformed Heisenberg algebra. This algebra…

In this paper we study a class of modules over infinite-dimensional Lie (super)algebras, which we call conformal modules. In particular we classify and construct explicitly all irreducible conformal modules over the Virasoro and the N=1…

Classes of algebraic structures that are defined by equational laws are called varieties or equational classes. A variety is finitely generated if it is defined by the laws that hold in some fixed finite algebra. We show that every…

We define nodal finite dimensional algebras and describe their structure over an algebraically closed field. For a special class of such algebras (type A) we find a criterion of tameness.

We give a classification of $5$- and $6$-dimensional complex one-generated nilpotent bicommutative algebras.

In this paper the algebra of invariants for the adjoint action of the unitriangular group in the nilradical of a parabolic subalgebra is studied. We prove that the algebra of invariants is finitely generated.

To a regular projection of a knot we associate a finite dimensional non-commutative associative algebra which is self-injective and special biserial.

We study pairs of finitely generated modules over a principal ideal domain and their corresponding matrix representations. We introduce equivalence relations for such pairs and determine invariants and canonical forms.

We study non-selfadjoint operator algebras that can be entirely understood via their finite-dimensional representations. In contrast with the elementary matricial description of finite-dimensional $\mathrm{C}^*$-algebras, in the…

The purpose of this paper is to introduce the notion of noncommutative BiHom-pre-Poisson algebra. Also we establish the bimodules and matched pairs of noncommutative BiHom-(pre)-Poisson algebras and related relevant properties are also…

We consider a family of all analytic and univalent functions in the unit disk of the form $f(z)=z+a_2z^2+a_3z^3+\cdots$. The aim of this article is to investigate the bounds of the difference of moduli of initial successive coefficients,…

We explore the possibility to derive basic calculus rules for some subdifferential constructions associated to set-valued maps between normed vector spaces. Then, we use these results in order to write optimality conditions for a special…