The classification of modular Lie superalgebras of type M
Lili Ma ; Liangyun Chen
Open Mathematics, Tome 13 (2015), / Harvested from The Polish Digital Mathematics Library

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.

Publié le : 2015-01-01
EUDML-ID : urn:eudml:doc:270027
@article{bwmeta1.element.doi-10_1515_math-2015-0025,
     author = {Lili Ma and Liangyun Chen},
     title = {The classification of modular Lie superalgebras of type M},
     journal = {Open Mathematics},
     volume = {13},
     year = {2015},
     zbl = {1310.17010},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_1515_math-2015-0025}
}
Lili Ma; Liangyun Chen. The classification of modular Lie superalgebras of type M. Open Mathematics, Tome 13 (2015) . http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_1515_math-2015-0025/

[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. | Zbl 0772.17007

[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] | Zbl 0317.17002

[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] | Zbl 1121.17011

[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] | Zbl 1329.17017

[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] | Zbl 1278.17022

[7] Q. Mu, Y.Z. Zhang, Infinite-dimensional Hamiltonian Lie superalgebras, Sci. China Math., 53(6)(2010)1625-1634. [WoS][Crossref] | Zbl 1271.17011

[8] Q. Mu, Y.Z. Zhang, Infinite-dimensional modular special odd contact superalgebras, J. Pure Appl. Algebra, 214(8) (2010)1456- 1468. [WoS][Crossref] | Zbl 1245.17010

[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] | Zbl 1219.17016

[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] | Zbl 1275.17035

[12] Y.Z. Zhang, H.C. Fu, Finite-dimensional Hamiltonian Lie superalgebras, Comm. Algebra, 30(6)(2002)2651-2673. [Crossref] | Zbl 1021.17017

[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] | Zbl 1131.17009

[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 | Zbl 1054.17502