Finite-dimensional simple modular Lie superalgebra M

Abstract

A new family of finite-dimensional simple modular Lie superalgebra M is constructed based on results of Y. Z. Zhang and Q. C. Zhang [J. Algebra, 2009, 321: 3601–3619]. The simplicity and generators of M are discussed and the derivation superalgebra of M is characterized. Furthermore, the invariance of the nonnatural filtration of M is determined by the method of minimal dimension of image spaces.

Keywords

Modular Lie superalgebra / derivation superalgebra / nonnatural filtration

References

[1] Celousov M J. Derivations of Lie algebras of Cartan-type. Izv Vyssh Uchebn Zaved Mat, 1970, 98: 126-134 (in Russian)

[2] Eldugue A. Lie superalgebras with semisimple even part. J Algebra, 1996, 183: 649-663

[3] Fei Q Y. On new simple Lie algebras of Shen Guangyu. Chin Ann Math Ser B, 1989, 10: 448-457

[4] Kac V G. Description of filtered Lie algebras with which graded Lie algebras of Cartan type are associated. Math USSR-Izv, 1974, 8: 801-835

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

[6] Kac V G. Classification of infinite-dimensional simple linearly compact Lie super-algebras. Adv Math, 1998, 139: 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: 176-205

[8] Ma F M, Zhang Q C. Derivation algebra of modular Lie superalgebra Kof Cartan-type. J Math (Wuhan), 2000, 20: 431-435 (in Chinese)

[9] Shen G Y. An intrinsic property of the Lie algebra K(m, n).Chin Ann Math Ser B, 1981, 2: 105-115

[10] Wang X L, Liu W D. Filtered Lie superalgebras of odd Hamiltonian type HO.Adv Math (China), 2007, 36: 710-720

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

[12] Xu X N, Chen L Y, Zhang Y Z. On the modular Lie superalgebra Ω.J Pure Appl Algebra, 2011, 215: 1093-1101

[13] Zhang Q C, Zhang Y Z. Derivation algebras of modular Lie superalgebras Wand S of Cartan-type. Acta Math Sci Ser B Engl Ed, 2000, 20: 137-144

[14] Zhang Y Z. Finite-dimensional Lie superalgebras of Cartan-type over field of prime characteristic. Chin Sci Bull, 1997, 42: 720-724

[15] Zhang Y Z, Fu H C. Finite dimensional Hamiltonian Lie superalgebras. Comm Algebra, 2002, 30: 2651-2673

[16] Zhang Y Z, Liu W D. Modular Lie superalgebras. Beijing: Science Press, 2004 (in Chinese)

[17] Zhang Y Z, Nan J Z. Finite-dimensional Lie superalgebras W(m, n, t) and S(m, n, t) of Cartan-type. Adv Math (China), 1998, 27: 240-246

[18] Zhang Y Z, Zhang Q C. Finite-dimensional modular Lie superalgebra Ω.J Algebra, 2009, 321: 3601-3619

RIGHTS & PERMISSIONS

2014 Higher Education Press and Springer-Verlag Berlin Heidelberg