On realizations of polynomial algebras with three generators via deformed oscillator algebras

Isaac, Phillip S. and Marquette, Ian (2014) On realizations of polynomial algebras with three generators via deformed oscillator algebras. Journal of Physics A: Mathematical and Theoretical, 47 20: 1-26. doi:10.1088/1751-8113/47/20/205203


Author Isaac, Phillip S.
Marquette, Ian
Title On realizations of polynomial algebras with three generators via deformed oscillator algebras
Journal name Journal of Physics A: Mathematical and Theoretical   Check publisher's open access policy
ISSN 1751-8113
1751-8121
Publication date 2014-05-23
Year available 2014
Sub-type Article (original research)
DOI 10.1088/1751-8113/47/20/205203
Open Access Status
Volume 47
Issue 20
Start page 1
End page 26
Total pages 26
Place of publication Bristol, United Kingdom
Publisher Institute of Physics Publishing
Collection year 2015
Language eng
Abstract We present the most general polynomial Lie algebra generated by a second order integral of motion and one of order M, construct the Casimir operator, and show how the Jacobi identity provides the existence of a realization in terms of deformed oscillator algebra. We also present the classical analogue of this construction for the most general polynomial Poisson algebra. Two specific classes of such polynomial algebras are discussed that include the symmetry algebras observed for various 2D superintegrable systems.
Keyword Polynomial Lie algebra
Deformed oscillator algebra
Oscillator realization
Superintegrability
Superintegrable systems
Q-Index Code C1
Q-Index Status Confirmed Code
Institutional Status UQ

Document type: Journal Article
Sub-type: Article (original research)
Collections: School of Mathematics and Physics
Official 2015 Collection
 
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Citation counts: TR Web of Science Citation Count  Cited 6 times in Thomson Reuters Web of Science Article | Citations
Scopus Citation Count Cited 6 times in Scopus Article | Citations
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