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2015 | 13 | 1 |
Tytuł artykułu

The classification of modular Lie superalgebras of type M

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
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.
Wydawca
Czasopismo
Rocznik
Tom
13
Numer
1
Opis fizyczny
Daty
otrzymano
2014-08-03
zaakceptowano
2015-02-17
online
2015-03-04
Twórcy
autor
  • School of Mathematics and Statistics, Northeast Normal University, Changchun 130024, China, and School of Science, Qiqihar
    University, Qiqihar 161006, China
  • School of Mathematics and Statistics, Northeast Normal University, Changchun 130024,
    China
Bibliografia
  • [1] N. Jin, Ad-Nilpotent, quasi-nilpotent elements and invariant filtrations of infinite-dimensional Lie algebras of Cartan type, Sci.China (Ser. A), 35(10)(1992) 1191-1200.
  • [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]
  • [3] A.I. Kostrikin, I.R. Shafarevic, Graded Lie algebras of finite characteristic, Math. USSR, Izv, 3(1969)237-304.[Crossref]
  • [4] W.D. Liu, Y.Z. Zhang, Infinite-dimensional modular odd Hamiltonian superalgebras, Comm. Algebra, 32(6)(2004)2341-2357.[Crossref]
  • [5] L.L. Ma, L.Y. Chen, Y.Z. Zhang, Finite-dimensional simple modular Lie superalgebra M, Front. Math. China, 8(2)(2013)411-441.[WoS][Crossref]
  • [6] Q. Mu, L. Ren, Y.Z. Zhang, Ad-nilpotent elements, isomorphisms, and the Weisfeiler filtration of infinite-dimensional modular oddcontact superalgebras, Comm. Algebra, 39(10)(2011)3581-3593.[Crossref]
  • [7] Q. Mu, Y.Z. Zhang, Infinite-dimensional Hamiltonian Lie superalgebras, Sci. China Math., 53(6)(2010)1625-1634.[WoS][Crossref]
  • [8] Q. Mu, Y.Z. Zhang, Infinite-dimensional modular special odd contact superalgebras, J. Pure Appl. Algebra, 214(8) (2010)1456-1468.[WoS][Crossref]
  • [9] G.Y. Shen, An intrinsic property of the Lie algebra K.m; n/; Chin. Ann. Math., 2(1981)104-107.
  • [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]
  • [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]
  • [12] Y.Z. Zhang, H.C. Fu, Finite-dimensional Hamiltonian Lie superalgebras, Comm. Algebra, 30(6)(2002)2651-2673.[Crossref]
  • [13] Y.Z. Zhang, W.D. Liu, Infinite-dimensional modular Lie superalgebras W and S of Cartan type, Algebra Colloq., 13(2)(2006)197-210.[Crossref]
  • [14] Y.Z. Zhang, J.Z. Nan, Finite dimensional Lie superalgebras W.m; n; t/ and S.m; n; t/ of Cartan type, Chin. Adv. Math.,27(3)(1998)240-246
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_1515_math-2015-0025
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