An extension of a \(q\)-deformed Heisenberg algebra and its Lie polynomials

DOI10.1016/j.exmath.2019.12.001zbMath1502.16024arXiv1812.06757OpenAlexW3000018595WikidataQ115353671 ScholiaQ115353671MaRDI QIDQ2035552

Mark Anthony C. Merciales, Rafael Reno S. Cantuba

Publication date: 25 June 2021

Published in: Expositiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1812.06757

zbMATH Keywords

central extensiondiamond lemma\(q\)-deformed Heisenberg algebraLie polynomial

Mathematics Subject Classification ID

Finite generation, finite presentability, normal forms (diamond lemma, term-rewriting) (16S15) Lie (super)algebras associated with other structures (associative, Jordan, etc.) (17B60) Operator algebras with symbol structure (47L15) Individual linear operators as elements of algebraic systems (47C99)

Related Items (5)

Recent developments in combinatorial aspects of normal ordering ⋮ Lie polynomials in an algebra defined by a linearly twisted commutation relation ⋮ Lie structure of the Heisenberg-Weyl algebra ⋮ Frattinian nilpotent Lie algebras ⋮ A CASIMIR ELEMENT INEXPRESSIBLE AS A LIE POLYNOMIAL

Cites Work

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• The universal Askey-Wilson algebra
• The diamond lemma for ring theory
• On spectral properties of \(q\)-oscillator operators
• Lie polynomials in \(q\)-deformed Heisenberg algebras
• Two-sided ideals in \(q\)-deformed Heisenberg algebras.
• On q-analogues of the quantum harmonic oscillator and the quantum group SU(2)_q
• The quantum group SU_q(2) and a q-analogue of the boson operators
• REPRESENTATIONS OF THE ANTICOMMUTATION RELATIONS
• REPRESENTATIONS OF THE COMMUTATION RELATIONS

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