The classification of modular Lie superalgebras of type M

• Autorzy: Lili Ma , Liangyun Chen
• 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.

Słowa kluczowe

EN

Modular Lie superalgebra; Ad-nilpotent element; Filtration

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2015
• Tom: 13
• Numer: 1

Daty

otrzymano

2014-08-03

zaakceptowano

2015-02-17

online

2015-03-04

Twórcy

autor

Lili Ma

• School of Mathematics and Statistics, Northeast Normal University, Changchun 130024, China, and School of Science, Qiqihar
  University, Qiqihar 161006, China

autor

Liangyun Chen

• 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 odd contact 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

Identyfikatory

DOI

10.1515/math-2015-0025