Matrix Bosonic realizations of a Lie colour algebra with three generators and five relations of Heisenberg Lie type
Sigurdsson, Gunnar ; Silvestrov, Sergei D.
J. Gen. Lie Theory Appl., Tome 3 (2009) no. 3, p. 329-340 / Harvested from Project Euclid
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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.
Publié le : 2009-12-15
Classification:  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,  17B75,  16G99,  16S32,  34K99,  81S05 
@article{1281106600,
     author = {Sigurdsson, Gunnar and Silvestrov, Sergei D.},
     title = {Matrix Bosonic realizations of a Lie colour algebra with three generators and
 five relations of Heisenberg Lie type},
     journal = {J. Gen. Lie Theory Appl.},
     volume = {3},
     number = {3},
     year = {2009},
     pages = { 329-340},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1281106600}
}

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., Tome 3 (2009) no. 3, pp.  329-340. http://gdmltest.u-ga.fr/item/1281106600/