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Parabosons, parafermions and representations of ℤ₂ x ℤ₂-graded Lie superalgebras

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Abstract
For a set of m parafermion operators and n paraboson operators, there are two nontrivial ways to unify them in a larger algebraic structure. One of these corresponds to the orthosymplectic Lie superalgebra osp(2m + 1 vertical bar 2n). The other one is no longer a Z(2)-graded Lie superalgebra but a Z(2) x Z(2)-graded Lie superalgebra, a rather different algebraic structure, denoted here by pso(2m + 1 vertical bar 2n). In a recent paper, the Fock spaces (V) over tilde (p) of order p for pso(2m+1 vertical bar 2n) were determined. In the current paper, we summarize some of the main properties of pso(2m+1 vertical bar 2n) and its Fock spaces. In particular, we concentrate on the Fock space for p = 1, and indicate how it reduces to an ordinary boson-fermion Fock space.
Keywords
parabosons, parafermions, orthosymplectic Lie superalgebra, Lie superalgebras, parastatistics, PARA-BOSE

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MLA
Stoilova, N. I., and Joris Van der Jeugt. “Parabosons, Parafermions and Representations of ℤ₂ x ℤ₂-Graded Lie Superalgebras.” 32ND INTERNATIONAL COLLOQUIUM ON GROUP THEORETICAL METHODS IN PHYSICS (GROUP32), vol. 1194, Iop Publishing Ltd, 2019, doi:10.1088/1742-6596/1194/1/012102.
APA
Stoilova, N. I., & Van der Jeugt, J. (2019). Parabosons, parafermions and representations of ℤ₂ x ℤ₂-graded Lie superalgebras. In 32ND INTERNATIONAL COLLOQUIUM ON GROUP THEORETICAL METHODS IN PHYSICS (GROUP32) (Vol. 1194). Prague, CZECH REPUBLIC: Iop Publishing Ltd. https://doi.org/10.1088/1742-6596/1194/1/012102
Chicago author-date
Stoilova, N. I., and Joris Van der Jeugt. 2019. “Parabosons, Parafermions and Representations of ℤ₂ x ℤ₂-Graded Lie Superalgebras.” In 32ND INTERNATIONAL COLLOQUIUM ON GROUP THEORETICAL METHODS IN PHYSICS (GROUP32). Vol. 1194. Iop Publishing Ltd. https://doi.org/10.1088/1742-6596/1194/1/012102.
Chicago author-date (all authors)
Stoilova, N. I., and Joris Van der Jeugt. 2019. “Parabosons, Parafermions and Representations of ℤ₂ x ℤ₂-Graded Lie Superalgebras.” In 32ND INTERNATIONAL COLLOQUIUM ON GROUP THEORETICAL METHODS IN PHYSICS (GROUP32). Vol. 1194. Iop Publishing Ltd. doi:10.1088/1742-6596/1194/1/012102.
Vancouver
1.
Stoilova NI, Van der Jeugt J. Parabosons, parafermions and representations of ℤ₂ x ℤ₂-graded Lie superalgebras. In: 32ND INTERNATIONAL COLLOQUIUM ON GROUP THEORETICAL METHODS IN PHYSICS (GROUP32). Iop Publishing Ltd; 2019.
IEEE
[1]
N. I. Stoilova and J. Van der Jeugt, “Parabosons, parafermions and representations of ℤ₂ x ℤ₂-graded Lie superalgebras,” in 32ND INTERNATIONAL COLLOQUIUM ON GROUP THEORETICAL METHODS IN PHYSICS (GROUP32), Prague, CZECH REPUBLIC, 2019, vol. 1194.
@inproceedings{8668569,
  abstract     = {{For a set of m parafermion operators and n paraboson operators, there are two nontrivial ways to unify them in a larger algebraic structure. One of these corresponds to the orthosymplectic Lie superalgebra osp(2m + 1 vertical bar 2n). The other one is no longer a Z(2)-graded Lie superalgebra but a Z(2) x Z(2)-graded Lie superalgebra, a rather different algebraic structure, denoted here by pso(2m + 1 vertical bar 2n). In a recent paper, the Fock spaces (V) over tilde (p) of order p for pso(2m+1 vertical bar 2n) were determined. In the current paper, we summarize some of the main properties of pso(2m+1 vertical bar 2n) and its Fock spaces. In particular, we concentrate on the Fock space for p = 1, and indicate how it reduces to an ordinary boson-fermion Fock space.}},
  articleno    = {{012102}},
  author       = {{Stoilova, N. I. and Van der Jeugt, Joris}},
  booktitle    = {{32ND INTERNATIONAL COLLOQUIUM ON GROUP THEORETICAL METHODS IN PHYSICS (GROUP32)}},
  issn         = {{1742-6588}},
  keywords     = {{parabosons,parafermions,orthosymplectic Lie superalgebra,Lie superalgebras,parastatistics,PARA-BOSE}},
  language     = {{eng}},
  location     = {{Prague, CZECH REPUBLIC}},
  pages        = {{9}},
  publisher    = {{Iop Publishing Ltd}},
  title        = {{Parabosons, parafermions and representations of ℤ₂ x ℤ₂-graded Lie superalgebras}},
  url          = {{http://dx.doi.org/10.1088/1742-6596/1194/1/012102}},
  volume       = {{1194}},
  year         = {{2019}},
}

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