Some properties of the family Γ of modular Lie superalgebras

Xiaoning Xu; Liangyun Chen

Czechoslovak Mathematical Journal (2013)

  • Volume: 63, Issue: 4, page 1087-1112
  • ISSN: 0011-4642

Abstract

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In this paper, we continue to investigate some properties of the family Γ of finite-dimensional simple modular Lie superalgebras which were constructed by X. N. Xu, Y. Z. Zhang, L. Y. Chen (2010). For each algebra in the family, a filtration is defined and proved to be invariant under the automorphism group. Then an intrinsic property is proved by the invariance of the filtration; that is, the integer parameters in the definition of Lie superalgebras Γ are intrinsic. Thereby, we classify these Lie superalgebras in the sense of isomorphism. Finally, we study the associative forms and Killing forms of these Lie superalgebras and determine which superalgebras in the family are restrictable.

How to cite

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Xu, Xiaoning, and Chen, Liangyun. "Some properties of the family $\Gamma $ of modular Lie superalgebras." Czechoslovak Mathematical Journal 63.4 (2013): 1087-1112. <http://eudml.org/doc/260787>.

@article{Xu2013,
abstract = {In this paper, we continue to investigate some properties of the family $\Gamma $ of finite-dimensional simple modular Lie superalgebras which were constructed by X. N. Xu, Y. Z. Zhang, L. Y. Chen (2010). For each algebra in the family, a filtration is defined and proved to be invariant under the automorphism group. Then an intrinsic property is proved by the invariance of the filtration; that is, the integer parameters in the definition of Lie superalgebras $\Gamma $ are intrinsic. Thereby, we classify these Lie superalgebras in the sense of isomorphism. Finally, we study the associative forms and Killing forms of these Lie superalgebras and determine which superalgebras in the family are restrictable.},
author = {Xu, Xiaoning, Chen, Liangyun},
journal = {Czechoslovak Mathematical Journal},
keywords = {modular Lie superalgebra; restricted Lie superalgebra; filtration; modular Lie superalgebra; restricted Lie superalgebra; filtration},
language = {eng},
number = {4},
pages = {1087-1112},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Some properties of the family $\Gamma $ of modular Lie superalgebras},
url = {http://eudml.org/doc/260787},
volume = {63},
year = {2013},
}

TY - JOUR
AU - Xu, Xiaoning
AU - Chen, Liangyun
TI - Some properties of the family $\Gamma $ of modular Lie superalgebras
JO - Czechoslovak Mathematical Journal
PY - 2013
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 63
IS - 4
SP - 1087
EP - 1112
AB - In this paper, we continue to investigate some properties of the family $\Gamma $ of finite-dimensional simple modular Lie superalgebras which were constructed by X. N. Xu, Y. Z. Zhang, L. Y. Chen (2010). For each algebra in the family, a filtration is defined and proved to be invariant under the automorphism group. Then an intrinsic property is proved by the invariance of the filtration; that is, the integer parameters in the definition of Lie superalgebras $\Gamma $ are intrinsic. Thereby, we classify these Lie superalgebras in the sense of isomorphism. Finally, we study the associative forms and Killing forms of these Lie superalgebras and determine which superalgebras in the family are restrictable.
LA - eng
KW - modular Lie superalgebra; restricted Lie superalgebra; filtration; modular Lie superalgebra; restricted Lie superalgebra; filtration
UR - http://eudml.org/doc/260787
ER -

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