Related papers: Polymorphism of Representations of Universal Algeb…
We introduce representations of the Cuntz algebra $\con$ which are parameterized by sequences in the set of unit vectors in ${\bf C}^{N}$. These representations are natural generalizations of permutative representations by…
We study linear maps preserving the higher numerical ranges of tensor product of matrices.
In this paper we study the tensor product of two $f$-algebras. We show that the Riesz Subspace generated by a subalgebra in an $f$-algebra is an algebra in order to prove that the Riesz tensor product of two $f$-algebras has a structure of…
Computer algebra is widely used in various fields of mathematics, physics and other sciences. The simplification of tensor expressions is an important special case of computer algebra. In this paper, we consider the reduction of tensor…
This is the central article of a series of three papers on cross product bialgebras. We present a universal theory of bialgebra factorizations (or cross product bialgebras) with cocycles and dual cocycles. We also provide an equivalent…
We show that two tensor permutation matrices permutate tensor product of rectangle matrices. Some examples, in the particular case of tensor commutation matrices, for studying some linear matrix equations are given.
In this paper we study the complete reducibility of representations of infinite-dimensional Lie algebras from the perspective of the representation theory of vertex algebras.
We establish relations between representation dimensions of two algebras connected by a Frobenius bimodule or extension. Consequently, upper bounds and equality formulas for representation dimensions of group algebras, symmetric separably…
It is well known that the cohomology of a tensor product is essentially the tensor product of the cohomologies. We look at twisted tensor products, and investigate to which extend this is still true. We give an explicit description of the…
This paper studies unitary representations with Dirac cohomology for complex groups, in particular relations to unipotent representations
We introduce the notion of a generalized representation of a Jordan algebra with unit. The greneralized representation has the following properties: (1) Usual representations and Jacobson representations correspond to special cases of…
Important characteristics of the loop approach to quantum gravity are a specific choice of the algebra A of observables and of a representation of A on a measure space over the space of generalized connections. This representation is…
We construct the augmentation representation. It is a representation of the fundamental group of the link complement associated to an augmentation of the framed cord algebra. This construction connects representations of two link invariants…
For a representation of a Lie algebra, one can construct a diagram of the representation, i. e. a directed graph with edges labeled by matrix elements of the representation. This article explains how to use these diagrams to describe normal…
We show that every partial representation of a connected Hopf algebra is global. Some interesting classes of partial representations of smash product Hopf algebras are studied, and a description of the partial "Hopf" algebra if the first…
In this paper we consider a special class of polymorphisms with invariant measure, - (cf.[1])- the algebraic polymorphisms of compact groups. A general polymorphism is -- by definition -- a many-valued map with invariant measure, and the…
In this paper we study universal central extensions and non-abelian tensor product of hom-Lie-Rinehart algebras. We discuss about universal $\alpha$- central extensions, and, lifting of automorphisms and $\alpha$-derivations to central…
Pseudoalgebras, introduced in [BDK], are multi-dimensional analogues of conformal algebras, which provide an axiomatic description of the singular part of the operator product expansion. Our main interest in this paper is the pseudoalgebra…
We introduce the notion of ``finite general representation type'' for a finite-dimensional algebra, a property related to the ``dense orbit property'' introduced by Chindris-Kinser-Weyman. We use an interplay of geometric, combinatorial,…
In recent years, the notion of characteristic polynomial of representations of Lie algebras has been widely studied. This paper provides more properties of these characteristic polynomials. For simple Lie algebras, we characterize the…