The classification of modular Lie superalgebras of type M

Lili Ma; Liangyun Chen

Open Mathematics (2015)

  • Volume: 13, Issue: 1, page 279-292
  • ISSN: 2391-5455

Abstract

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The natural filtration of the infinite-dimensional simple modular Lie superalgebra M over a field of characteristic p > 2 is proved to be invariant under automorphisms by discussing ad-nilpotent elements. Moreover, an intrinsic property is obtained and all the infinite-dimensional simple modular Lie superalgebras M are classified up to isomorphisms. As an application, a property of automorphisms of M is given.

How to cite

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Lili Ma, and Liangyun Chen. "The classification of modular Lie superalgebras of type M." Open Mathematics 13.1 (2015): 279-292. <http://eudml.org/doc/270027>.

@article{LiliMa2015,
abstract = {The natural filtration of the infinite-dimensional simple modular Lie superalgebra M over a field of characteristic p > 2 is proved to be invariant under automorphisms by discussing ad-nilpotent elements. Moreover, an intrinsic property is obtained and all the infinite-dimensional simple modular Lie superalgebras M are classified up to isomorphisms. As an application, a property of automorphisms of M is given.},
author = {Lili Ma, Liangyun Chen},
journal = {Open Mathematics},
keywords = {Modular Lie superalgebra; Ad-nilpotent element; Filtration; modular Lie superalgebra; derivation algebra; generator sets},
language = {eng},
number = {1},
pages = {279-292},
title = {The classification of modular Lie superalgebras of type M},
url = {http://eudml.org/doc/270027},
volume = {13},
year = {2015},
}

TY - JOUR
AU - Lili Ma
AU - Liangyun Chen
TI - The classification of modular Lie superalgebras of type M
JO - Open Mathematics
PY - 2015
VL - 13
IS - 1
SP - 279
EP - 292
AB - The natural filtration of the infinite-dimensional simple modular Lie superalgebra M over a field of characteristic p > 2 is proved to be invariant under automorphisms by discussing ad-nilpotent elements. Moreover, an intrinsic property is obtained and all the infinite-dimensional simple modular Lie superalgebras M are classified up to isomorphisms. As an application, a property of automorphisms of M is given.
LA - eng
KW - Modular Lie superalgebra; Ad-nilpotent element; Filtration; modular Lie superalgebra; derivation algebra; generator sets
UR - http://eudml.org/doc/270027
ER -

References

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  2. [2] V.G. Kac, Description of filtered Lie algebras with which graded Lie algebras of Cartan type are associated, Math. USSR, Izv., 8(1974)801-835. [Crossref] Zbl0317.17002
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  10. [10] X.N. Xu, L.Y. Chen, Y.Z. Zhang, On the modular Lie superalgebra , J. Pure Appl. Algebra, 215(5)(2011)1093-1101. [WoS][Crossref] Zbl1219.17016
  11. [11] J.X. Yuan, W.D. Liu, Fitration, automorphisms and classification of the infinite dimensional odd Contact superalgebras, Front. Math. China, 8(1)(2013)203-216. [WoS][Crossref] Zbl1275.17035
  12. [12] Y.Z. Zhang, H.C. Fu, Finite-dimensional Hamiltonian Lie superalgebras, Comm. Algebra, 30(6)(2002)2651-2673. [Crossref] Zbl1021.17017
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