Representation Theory of Finite-Dimensional Algebras

Representation theory of finite dimensional algebras

Representation Theory of Three-dimensional Sklyanin Algebras

Abstract. We determine the dimensions of the irreducible representations of the Sklyanin algebras with global dimension 3. This contributes to the study of marginal deformations of the N=4 super Yang-Mills theory in four dimensions in supersymmetric string theory. Namely, the classification of such representations is equivalent to determining the vacua of the aforementioned deformed theories. W...

Affine.m - Mathematica package for computations in representation theory of finite-dimensional and affine Lie algebras

In this paper we present Affine.m — a program for computations in representation theory of finite-dimensional and affine Lie algebras and describe implemented algorithms. The algorithms are based on the properties of weights and Weyl symmetry. Computation of weight multiplicities in irreducible and Verma modules, branching of representations and tensor product decomposition are the most importa...

Invariant Means and Finite Representation Theory of C-algebras

Various subsets of the tracial state space of a unital C∗-algebra are studied. The largest of these subsets has a natural interpretation as the space of invariant means. II1-factor representations of a class of C ∗-algebras considered by Sorin Popa are also studied. These algebras are shown to have an unexpected variety of II1-factor representations. This general theory is related to various ot...

On permutably complemented subalgebras of finite dimensional Lie algebras

Let $L$ be a finite-dimensional Lie algebra. We say a subalgebra $H$ of $L$ is permutably complemented in $L$ if there is a subalgebra $K$ of $L$ such that $L=H+K$ and $Hcap K=0$. Also, if every subalgebra of $L$ is permutably complemented in $L$, then $L$ is called completely factorisable. In this article, we consider the influence of these concepts on the structure of a Lie algebra, in partic...