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

被引：4
|
作者：
Cantuba, Rafael Reno S. [1 ]
Merciales, Mark Anthony C. [1 ]
机构：
[1] De La Salle Univ, Math & Stat Dept, Manila, Philippines
来源：
EXPOSITIONES MATHEMATICAE | 2021年 / 39卷 / 01期
关键词：
q-deformed Heisenberg algebra; Diamond lemma; Lie polynomial; Central extension; OSCILLATOR;
D O I：
10.1016/j.exmath.2019.12.001
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Let F be a field, and fix a q is an element of F. The q-deformed Heisenberg algebra H(q) is the unital associative algebra over F with generators A, B and a relation which asserts that AB - qB A is the multiplicative identity in H(q). We extend H(q) into an algebra R(q) defined by generators A, B and a relation which asserts that AB - qB A is central in R(q). We identify all elements of R(q) that are Lie polynomials in A, B. (C) 2020 Elsevier GmbH. All rights reserved.
引用
收藏
页码：1 / 24
页数：24
相关论文
共 50 条
  • [41] Knot polynomials from q-deformed algebras
    Smithies, CR
    Butler, PH
    [J]. JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 1996, 29 (19): : 6413 - 6428
  • [42] Weakly q-deformed Heisenberg algebra and non-Hermitian Hamiltonians: Application in statistical physics
    Moulla, Hafida
    Bouaziz, Djamil
    Aissaoui, Habib
    Mebarki, Noureddine
    [J]. NUCLEAR PHYSICS B, 2024, 1006
  • [43] Embedding q-deformed Heisenberg algebras into undeformed ones
    Fiore, G
    [J]. REPORTS ON MATHEMATICAL PHYSICS, 1999, 43 (1-2) : 101 - 108
  • [44] q-deformed Hermite polynomials in q-quantum mechanics
    Hinterding, R
    Wess, J
    [J]. EUROPEAN PHYSICAL JOURNAL C, 1999, 6 (01): : 183 - 186
  • [45] q-deformed dynamics of q-deformed oscillators
    Gruver, JL
    [J]. PHYSICS LETTERS A, 1999, 254 (1-2) : 1 - 6
  • [46] q-deformed fuzzy Ginsparg-Wilson algebra and its q-deformed Dirac and chirality operators on quantum fuzzy two-sphere
    Lotfizadeh, M.
    Asl, Ebrahim Nouri
    [J]. INTERNATIONAL JOURNAL OF GEOMETRIC METHODS IN MODERN PHYSICS, 2020, 17 (10)
  • [47] New q-Deformed Oscillator Algebra and Thermodynamic Model
    Won Sang Chung
    [J]. International Journal of Theoretical Physics, 2014, 53 : 426 - 434
  • [48] Quantum Group Structure of the q-Deformed Virasoro Algebra
    Hu N.
    [J]. Letters in Mathematical Physics, 1998, 44 (2) : 99 - 103
  • [49] q-deformed fermions:: Algebra, fock space and thermodynamics
    Swamy, P. Narayana
    [J]. INTERNATIONAL JOURNAL OF MODERN PHYSICS B, 2006, 20 (18): : 2537 - 2550
  • [50] Low-dimensional cohomology of q-deformed Heisenberg-Virasoro algebra of Hom-type
    Cheng, Yongsheng
    Yang, Hengyun
    [J]. FRONTIERS OF MATHEMATICS IN CHINA, 2010, 5 (04) : 607 - 622
12345