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On structure and TKK algebras for Jordan superalgebras

(2018) COMMUNICATIONS IN ALGEBRA. 46(2). p.684-704
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Abstract
We compare a number of different definitions of structure algebras and TKK constructions for Jordan (super)algebras appearing in the literature. We demonstrate that, for unital superalgebras, all the definitions of the structure algebra and the TKK constructions reduce to one of two cases. Moreover, one can be obtained as the Lie superalgebra of superderivations of the other. We also show that, for non-unital superalgebras, more definitions become nonequivalent. As an application, we obtain the corresponding Lie superalgebras for all simple finite dimensional Jordan superalgebras over an algebraically closed field of characteristic zero.
Keywords
Lie superalgebras, Jordan superalgebras, TKK-construction

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MLA
Barbier, Sigiswald, and Kevin Coulembier. “On Structure and TKK Algebras for Jordan Superalgebras.” COMMUNICATIONS IN ALGEBRA 46.2 (2018): 684–704. Print.
APA
Barbier, S., & Coulembier, K. (2018). On structure and TKK algebras for Jordan superalgebras. COMMUNICATIONS IN ALGEBRA, 46(2), 684–704.
Chicago author-date
Barbier, Sigiswald, and Kevin Coulembier. 2018. “On Structure and TKK Algebras for Jordan Superalgebras.” Communications in Algebra 46 (2): 684–704.
Chicago author-date (all authors)
Barbier, Sigiswald, and Kevin Coulembier. 2018. “On Structure and TKK Algebras for Jordan Superalgebras.” Communications in Algebra 46 (2): 684–704.
Vancouver
1.
Barbier S, Coulembier K. On structure and TKK algebras for Jordan superalgebras. COMMUNICATIONS IN ALGEBRA. 530 WALNUT STREET, STE 850, PHILADELPHIA, PA 19106 USA: TAYLOR & FRANCIS INC; 2018;46(2):684–704.
IEEE
[1]
S. Barbier and K. Coulembier, “On structure and TKK algebras for Jordan superalgebras,” COMMUNICATIONS IN ALGEBRA, vol. 46, no. 2, pp. 684–704, 2018.
@article{8545236,
  abstract     = {We compare a number of different definitions of structure algebras and TKK constructions for Jordan (super)algebras appearing in the literature. We demonstrate that, for unital superalgebras, all the definitions of the structure algebra and the TKK constructions reduce to one of two cases. Moreover, one can be obtained as the Lie superalgebra of superderivations of the other. We also show that, for non-unital superalgebras, more definitions become nonequivalent. As an application, we obtain the corresponding Lie superalgebras for all simple finite dimensional Jordan superalgebras over an algebraically closed field of characteristic zero.},
  author       = {Barbier, Sigiswald and Coulembier, Kevin},
  issn         = {0092-7872},
  journal      = {COMMUNICATIONS IN ALGEBRA},
  keywords     = {Lie superalgebras,Jordan superalgebras,TKK-construction},
  language     = {eng},
  number       = {2},
  pages        = {684--704},
  publisher    = {TAYLOR & FRANCIS INC},
  title        = {On structure and TKK algebras for Jordan superalgebras},
  url          = {http://dx.doi.org/10.1080/00927872.2017.1327059},
  volume       = {46},
  year         = {2018},
}

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