Matrix Bosonic realizations of a Lie colour algebra with three generators and ve relations of Heisenberg Lie type

Gunnar SIGURDSSON a and Ser

Abstract

We describe realizations of a Lie colour algebra with three generators and ve relations by matrices of power series in noncommuting indeterminates satisfying Heisenberg's canonical commutation relation of quantum mechanics. The obtained formulas are used to construct new operator representations of this Lie colour algebra using canonical representation of the Heisenberg commutation relation and creation and annihilation operators of the quantum mechanical harmonic oscillator.