Journal of Generalized Lie Theory and Applications

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

Gunnar Sigurdsson and Sergei D. Silvestrov

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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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J. Gen. Lie Theory Appl., Volume 3, Number 4 (2009), 329-340.

First available in Project Euclid: 6 August 2010

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Primary: 17B75: Color Lie (super)algebras 16G99: None of the above, but in this section 16S32: Rings of differential operators [See also 13N10, 32C38] 34K99: None of the above, but in this section 81S05: Canonical quantization, commutation relations and statistics

Nonassociative Rings Nonassociative Algebras Color Lie Algebras Color Lie Superalgebras Associative Rings For The Commutative Case Associative Algebras For The Commutative Case Representation Theory Of Rings Rings Of Differential Operators Ordinary Differential Equations Functional-Differential Equations Differential-Difference Equations Quantum Theory General Quantum Mechanics General Problems Of Quantization Canonical Quantization Commutation Relations And Statistics


Sigurdsson, Gunnar; Silvestrov, Sergei D. Matrix Bosonic realizations of a Lie colour algebra with three generators and five relations of Heisenberg Lie type. J. Gen. Lie Theory Appl. 3 (2009), no. 4, 329--340. doi:10.4303/jglta/S090406.

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