Quantized GIM Lie algebras and their Lusztig symmetries

Quantized Affine Lie Algebras and Diagonalization of Braid Generators

Let Uq(Ĝ) be a quantized affine Lie algebra. It is proven that the universal R-matrix R of Uq(Ĝ) satisfies the celebrated conjugation relation R = TR with T the usual twist map. As applications, braid generators are shown to be diagonalizable on arbitrary tensor product modules of integrable irreducible highest weight Uq(Ĝ)-module and a spectral decomposition formula for the braid generators is...

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

Family of operators and their Lie algebras

Lie Algebras and their corresponding linear groups