Quantum Groups,Deformed Oscillators and their Interrelations

Abstract

The main notions of the quantum groups: coproduct, action and coaction, representation and corepresentation are discussed using simplest examples: $G{L}_q(2)$, $s{l}_q(2)$, $q$-oscillator algebra $\mathcal{A}(q)$, and reflection equation algebra. The Gauss decompositions of quantum groups and their realizations in terms of\, $\mathcal{A}(q)$ are given.

14p, LaTex

Cited by in corpus (3)

• Irreducible representations of deformed oscillator algebra and q-special functions
• Baxterization of GL_q(2) and its application to the Liouville model and some other models on a lattice
• Geometry of Deformed Boson Algebras