A class of generalized odd Hamiltonian Lie superalgebras

doi:10.1007/s11464-014-0415-1

Front. Math. China

2014, Vol. 9

Issue (5) : 1105-1129 https://doi.org/10.1007/s11464-014-0415-1

RESEARCH ARTICLE

A class of generalized odd Hamiltonian Lie superalgebras

Li REN¹,Qiang MU^2,^*(

),Yongzheng ZHANG³

1. School of Mathematics, Sichuan University, Chengdu 610064, China
2. School of Mathematical Sciences, Harbin Normal University, Harbin 150025, China
3. School of Mathematics and Statistics, Northeast Normal University, Changchun 130024, China

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Abstract

We study class of finite-dimensional Cantan-type Lie superalgebras HO(m) over a field of prime characteristic, which can be regarded as extensions of odd Hamiltonian superalgebra HO. And we also determine the derivation superalgebras of Lie superalgebras HO(m).

Keywords Derivation superalgebra modular Lie superalgebra Lie superalgebra of Cartan type

Corresponding Author(s): Qiang MU

Issue Date: 26 August 2014

Cite this article:

Li REN,Qiang MU,Yongzheng ZHANG. A class of generalized odd Hamiltonian Lie superalgebras[J]. Front. Math. China, 2014, 9(5): 1105-1129.

URL:

https://academic.hep.com.cn/fmc/EN/10.1007/s11464-014-0415-1
https://academic.hep.com.cn/fmc/EN/Y2014/V9/I5/1105

1	Celousov M J. Derivations of Lie algebras of Cartan-type. Izv Vyssh Uchebn Zaved Mat, 1970, 98(7): 126-134 (in Russian)
2	Farnsteiner R. Derivations and central extensions of finitely generated graded Lie algebras. J Algebra, 1988, 118(1): 33-45 doi: 10.1016/0021-8693(88)90046-4
3	Fu J Y, Zhang Q C, Jiang C P. The Cartan-type modular Lie superalgebra KO. Comm Algebra, 2006, 34(1): 107-128 doi: 10.1080/00927870500346065
4	Grabowski J, Poncin N. Derivations of the Lie algebras of differential operators. Indag Math (NS), 2005, 16(2): 181-200 doi: 10.1016/S0019-3577(05)80022-9
5	Kac V G. Lie superalgebras. Adv Math, 1977, 26(1): 8-96 doi: 10.1016/0001-8708(77)90017-2
6	Kac V G. Classification of infinite-dimensional simple linearly compact Lie superalgebras. Adv Math, 1998, 139(1): 1-55 doi: 10.1006/aima.1998.1756
7	Liu W D, Zhang Y Z, Wang X L. The derivation algebra of the Cartan-type Lie superalgebra HO. J Algebra, 2004, 273(1): 176-205 doi: 10.1016/j.jalgebra.2003.10.019
8	Liu W D, Zhang Y Z. Finite-dimensional odd Hamiltonian superalgebras over a field of prime characteristic. J Aust Math Soc, 2005, 79(1): 113-130 doi: 10.1017/S1446788700009368
9	Liu W D, Zhang Y Z. Automorphism groups of restricted Cartan-type Lie superalgebras. Comm Algebra, 2006, 34(10): 3767-3784 doi: 10.1080/00927870600862615
10	Ma L L, Chen L Y, Zhang Y Z. Finite-dimensional simple modular Lie superalgebra M. Front Math China, 2013, 8(2): 411-441 doi: 10.1007/s11464-012-0243-0
11	Petrogradski V M. Identities in the enveloping algebras for modular Lie superalgebras. J Algebra, 1992, 145(1): 1-21 doi: 10.1016/0021-8693(92)90173-J
12	Scheunert M. The Theory of Lie Superalgebras. Lecture Notes in Math, Vol 716. Berlin-Heidelberg-New York: Springer-Verlag, 1979
13	Shen G Y. New simple Lie algebras of characteristic p. Chinese Ann Math Ser B, 1983, 4(3): 329-346
14	Strade H, Farnsteiner R. Modular Lie a<?Pub Caret?>lgebras and their representations. Monographs and Textbooks in Pure and Applied Math, 116. New York: Marecl Dekker, Inc, 1988
15	Su Y C. Classification of finite-dimensional modules of the Lie superalgebras rmsl(2/1). Comm Algebra, 1992, 20(11): 3259-3278 doi: 10.1080/00927879208824514
16	Wang Y, Zhang Y Z. Derivation algebra Der(H) and central extensions of Lie superalgebras. Comm Algebra, 2004, 32(10): 4117-4131 doi: 10.1081/AGB-200029706
17	Xu X N, Zhang Y Z, Chen L Y. The finite-dimensional modular Lie superalgebra Г. Algebra Colloq, 2010, 17(3): 525-540 doi: 10.1142/S1005386710000507
18	Zhang Q C, Zhang Y Z. Derivation algebras of modular Lie superalgebras W and S of Cartan-type. Acta Math Sci, 2000, 20(1): 137-144
19	Zhang Y Z. Finite-dimensional Lie superalgebras of Cartan-type over field of prime characteristic. Chinese Sci Bull, 1997, 42(9): 720-724 doi: 10.1007/BF03186962
20	Zhang Y Z, Fu H C. Finite-dimensional Hamiltonian Lie superalgebra. Comm Algebra, 2002, 30(6): 2651-2673 doi: 10.1081/AGB-120003981
21	Zhang Y Z, Liu W D. Modular Lie Superalgebras. Beijing: Science Press, 2004 (in Chinese)
22	Zhang Y Z, Zhang Q C. The finite-dimensional modular Lie superalgebra Ω. J Algebra, 2009, 321(12): 3601-3619 doi: 10.1016/j.jalgebra.2009.01.038

[1]	Lili MA, Liangyun CHEN, Yongzheng ZHANG. Finite-dimensional simple modular Lie superalgebra M[J]. Front Math Chin, 2013, 8(2): 411-441.
[2]	Zhu WEI, Yongzheng ZHANG. Derivations for even part of finite-dimensional modular Lie superalgebra Ω?[J]. Front Math Chin, 2012, 7(6): 1169-1194.

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