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

Gunnar Sigurdsson; Sergei D. Silvestrov

doi:10.4303/jglta/S090406

December 2009 Matrix Bosonic realizations of a Lie colour algebra with three generators and five relations of Heisenberg Lie type

Gunnar Sigurdsson, Sergei D. Silvestrov

J. Gen. Lie Theory Appl. 3(4): 329-340 (December 2009). DOI: 10.4303/jglta/S090406

Abstract

We describe realizations of a Lie colour algebra with three generators and five 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.

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Gunnar Sigurdsson and Sergei D. Silvestrov "Matrix Bosonic realizations of a Lie colour algebra with three generators and five relations of Heisenberg Lie type," Journal of Generalized Lie Theory and Applications 3(4), 329-340, (December 2009). https://doi.org/10.4303/jglta/S090406

Published: December 2009

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