On Certain Quantum Deformations of $gl(N,R)$

Abstract

In this paper all deformations of the general linear group, subject to certain restrictions which in particular ensure a smooth passage to the Lie group limit, are obtained. Representations are given in terms of certains sets of creation and annihilation operators. These creation and annihilation operators may belong to a generalisation of the $q$-quark type or $q$-hadronic type, of $q$-boson or $q$-fermion type. We are also led to a natural definition of $q$-direct sums of q-algebras.

15 pages

References in corpus (5)

• Exchange Operator Formalism for Integrable Systems of Particles
• Explicit Solution to the N-Body Calogero Problem
• Braided Momentum Structure of the q-Poincare Group
• Operator Identities, Representations of Algebras and the Problem of Normal Ordering
• Study of Quommutators of Quantum Variables and Generalized Derivatives

Cited by in corpus (2)

• On some nonlinear extensions of the angular momentum algebra
• Quommutator deformations of spl(N,1)