A class of generalized odd Hamiltonian Lie superalgebras

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

References

[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

[3] Fu J Y, Zhang Q C, Jiang C P. The Cartan-type modular Lie superalgebra KO. Comm Algebra, 2006, 34(1): 107-128

[4] Grabowski J, Poncin N. Derivations of the Lie algebras of differential operators. Indag Math (NS), 2005, 16(2): 181-200

[5] Kac V G. Lie superalgebras. Adv Math, 1977, 26(1): 8-96

[6] Kac V G. Classification of infinite-dimensional simple linearly compact Lie superalgebras. Adv Math, 1998, 139(1): 1-55

[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

[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

[9] Liu W D, Zhang Y Z. Automorphism groups of restricted Cartan-type Lie superalgebras. Comm Algebra, 2006, 34(10): 3767-3784

[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

[11] Petrogradski V M. Identities in the enveloping algebras for modular Lie superalgebras. J Algebra, 1992, 145(1): 1-21

[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

[16] Wang Y, Zhang Y Z. Derivation algebra Der(H) and central extensions of Lie superalgebras. Comm Algebra, 2004, 32(10): 4117-4131

[17] Xu X N, Zhang Y Z, Chen L Y. The finite-dimensional modular Lie superalgebra Г. Algebra Colloq, 2010, 17(3): 525-540

[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

[20] Zhang Y Z, Fu H C. Finite-dimensional Hamiltonian Lie superalgebra. Comm Algebra, 2002, 30(6): 2651-2673

[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

RIGHTS & PERMISSIONS

2014 Higher Education Press and Springer-Verlag Berlin Heidelberg