On the Construction of Z2 × Z2- graded Lie colour algebras via Klein operators

Abstract

In this thesis, we study the structure and representation theory of certain colour Lie algebras. Precisely, we determine the existence of Z2 × Z2- graded colour variants of the Lie algebra gl(n) inside the quantum group Uq(gl(n)) in the limit as q → −1. This general linear algebra is realised via the Klein operators arising in the limit. Then, we study Z2 × Z2- graded colour embeddings of q-Schro ̈dinger algebra d = 1 in the limit q → −1, using previously developed methods.