Towers of semi-simple algebras

Combinatorial Hopf Algebras and Towers of Algebras

Bergeron and Li have introduced a set of axioms which guarantee that the Grothendieck groups of a tower of algebras L n≥0 An can be endowed with the structure of graded dual Hopf algebras. Hivert and Nzeutzhap, and independently Lam and Shimozono constructed dual graded graphs from primitive elements in Hopf algebras. In this paper we apply the composition of these constructions to towers of al...

Semi-simple Lie Algebras and Their Representations

This paper presents an overview of the representations of Lie algebras, particularly semi-simple Lie algebras, with a view towards theoretical physics. We proceed from the relationship between Lie algebras and Lie groups to more abstract characterizations of Lie groups, give basic definitions of different properties that may characterize Lie groups, and then prove results about root systems, pr...

Semi-Simple Lie Algebras and Their Representations

Semi-Simple Commutative Algebras with Positive Bases

Algebras that serve as models for concurrent studying of certain aspects of both the algebra of ordinary characters and the center of the group algebra have been considered by various authors. In this article we o¤er another such model. The main di¤erences between our model and the known ones are: 1. Our model includes Brauer characters and principal indecomposable characters as special cases. ...

Quantization of Cohomology in Semi-simple Lie Algebras

Let g be a complex, finite-dimensional Lie algebra, and Mo a contractable neighborhood of a complex homogeneous space on which g acts transitively. The present article investigates quantization of H(g; Cω(Mo)/C) by the condition that the corresponding realization by first-order operators admits a finitedimensional invariant subspace of functions. The quantization of cohomology phenomenon surfac...