Skip to content
BY-NC-ND 3.0 license Open Access Published by De Gruyter Open Access March 4, 2015

The classification of modular Lie superalgebras of type M

  • Lili Ma and Liangyun Chen
From the journal Open Mathematics

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.

References

[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. Search in Google Scholar

[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. 10.1070/IM1974v008n04ABEH002128Search in Google Scholar

[3] A.I. Kostrikin, I.R. Shafarevic, Graded Lie algebras of finite characteristic, Math. USSR, Izv, 3(1969)237-304. 10.1070/IM1969v003n02ABEH000766Search in Google Scholar

[4] W.D. Liu, Y.Z. Zhang, Infinite-dimensional modular odd Hamiltonian superalgebras, Comm. Algebra, 32(6)(2004)2341-2357. 10.1081/AGB-120037224Search in Google Scholar

[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. 10.1007/s11464-012-0243-0Search in Google Scholar

[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. 10.1080/00927872.2010.502162Search in Google Scholar

[7] Q. Mu, Y.Z. Zhang, Infinite-dimensional Hamiltonian Lie superalgebras, Sci. China Math., 53(6)(2010)1625-1634. 10.1007/s11425-010-3142-4Search in Google Scholar

[8] Q. Mu, Y.Z. Zhang, Infinite-dimensional modular special odd contact superalgebras, J. Pure Appl. Algebra, 214(8) (2010)1456- 1468. 10.1016/j.jpaa.2009.11.010Search in Google Scholar

[9] G.Y. Shen, An intrinsic property of the Lie algebra K.m; n/; Chin. Ann. Math., 2(1981)104-107. Search in Google Scholar

[10] X.N. Xu, L.Y. Chen, Y.Z. Zhang, On the modular Lie superalgebra , J. Pure Appl. Algebra, 215(5)(2011)1093-1101. 10.1016/j.jpaa.2010.07.014Search in Google Scholar

[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. 10.1007/s11464-012-0185-6Search in Google Scholar

[12] Y.Z. Zhang, H.C. Fu, Finite-dimensional Hamiltonian Lie superalgebras, Comm. Algebra, 30(6)(2002)2651-2673. 10.1081/AGB-120003981Search in Google Scholar

[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. 10.1142/S1005386706000204Search in Google Scholar

[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 Search in Google Scholar

Received: 2014-8-3
Accepted: 2015-2-17
Published Online: 2015-3-4

©2015 Lili Ma and Liangyun Chen

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Downloaded on 5.2.2023 from https://www.degruyter.com/document/doi/10.1515/math-2015-0025/html
Scroll Up Arrow