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The Z2xZ2-graded general linear Lie superalgebra

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Abstract
We present a novel realization of the Z2xZ2-graded Lie superalgebra gl(m1,m2|n1,n2) inside an algebraic extension of the enveloping algebra of the Z2-graded Lie superalgebra gl(m|n), with m = m(1) + m(2) and n = n(1) + n(2). A consequence of this realization is that the representations of gl(m|n) "lift up" to representations of gl(m1,m2|n1,n2), with matrix elements differing only by a sign, which we are able to characterize concisely.
Keywords
Lie superalgebras, color superalgebras, ALGEBRAS, CLASSIFICATION

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MLA
Isaac, Phillip S., et al. “The Z2xZ2-Graded General Linear Lie Superalgebra.” JOURNAL OF MATHEMATICAL PHYSICS, vol. 61, no. 1, 2020, doi:10.1063/1.5138597.
APA
Isaac, P. S., Stoilova, N. I., & Van der Jeugt, J. (2020). The Z2xZ2-graded general linear Lie superalgebra. JOURNAL OF MATHEMATICAL PHYSICS, 61(1). https://doi.org/10.1063/1.5138597
Chicago author-date
Isaac, Phillip S., N. I. Stoilova, and Joris Van der Jeugt. 2020. “The Z2xZ2-Graded General Linear Lie Superalgebra.” JOURNAL OF MATHEMATICAL PHYSICS 61 (1). https://doi.org/10.1063/1.5138597.
Chicago author-date (all authors)
Isaac, Phillip S., N. I. Stoilova, and Joris Van der Jeugt. 2020. “The Z2xZ2-Graded General Linear Lie Superalgebra.” JOURNAL OF MATHEMATICAL PHYSICS 61 (1). doi:10.1063/1.5138597.
Vancouver
1.
Isaac PS, Stoilova NI, Van der Jeugt J. The Z2xZ2-graded general linear Lie superalgebra. JOURNAL OF MATHEMATICAL PHYSICS. 2020;61(1).
IEEE
[1]
P. S. Isaac, N. I. Stoilova, and J. Van der Jeugt, “The Z2xZ2-graded general linear Lie superalgebra,” JOURNAL OF MATHEMATICAL PHYSICS, vol. 61, no. 1, 2020.
@article{8655232,
  abstract     = {{We present a novel realization of the Z2xZ2-graded Lie superalgebra gl(m1,m2|n1,n2) inside an algebraic extension of the enveloping algebra of the Z2-graded Lie superalgebra gl(m|n), with m = m(1) + m(2) and n = n(1) + n(2). A consequence of this realization is that the representations of gl(m|n) "lift up" to representations of gl(m1,m2|n1,n2), with matrix elements differing only by a sign, which we are able to characterize concisely.}},
  articleno    = {{011702}},
  author       = {{Isaac, Phillip S. and Stoilova, N. I. and Van der Jeugt, Joris}},
  issn         = {{0022-2488}},
  journal      = {{JOURNAL OF MATHEMATICAL PHYSICS}},
  keywords     = {{Lie superalgebras,color superalgebras,ALGEBRAS,CLASSIFICATION}},
  language     = {{eng}},
  number       = {{1}},
  pages        = {{7}},
  title        = {{The Z2xZ2-graded general linear Lie superalgebra}},
  url          = {{http://dx.doi.org/10.1063/1.5138597}},
  volume       = {{61}},
  year         = {{2020}},
}

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