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DERIVATIONS OF THE ODD CONTACT LIE ALGEBRAS IN PRIME CHARACTERISTIC
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 Title & Authors
DERIVATIONS OF THE ODD CONTACT LIE ALGEBRAS IN PRIME CHARACTERISTIC
Cao, Yan; Sun, Xiumei; Yuan, Jixia;
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 Abstract
The underlying field is of characteristic > 2. In this paper, we first use the method of computing the homogeneous derivations to determine the first cohomology of the so-called odd contact Lie algebra with coefficients in the even part of the generalized Witt Lie superalgebra. In particular, we give a generating set for the Lie algebra under consideration. Finally, as an application, the derivation algebra and outer derivation algebra of the Lie algebra are completely determined.
 Keywords
Lie superalgebra;derivation;first cohomology;
 Language
English
 Cited by
 References
1.
S. Bouarroudj, P. Grozman, and D. Leites, Classification of finite dimensional modular Lie superalgebras with indecomposable Cartan matrix, Symmetry Integrability Geom. Methods Appl. 5 (2009), 63 pages.

2.
S. Bouarroudj and D. Leites, Simple Lie superalgebras and nonintegrable distributions in characteristic p, J. Math. Sci. 141 (2007), no. 4, 1390-1398. crossref(new window)

3.
M. J. Celousov, Derivations of Lie algebras of Cartan type, Izv. Vyssh. Uchebn. Zaved. Mat. 98 (1970), 126-134.

4.
J.-Y. Fu, Q.-C. Zhang, and C.-P. Jiang, The Cartan-type modular Lie superalgebra KO, Comm. Algebra 34 (2006), no. 1, 107-128. crossref(new window)

5.
V. G. Kac, Lie superalgebras, Adv. Math. 26 (1977), no. 1, 8-96. crossref(new window)

6.
W.-D. Liu and B.-L. Guan, Derivations from the even parts into the odd parts for Lie superalgebras W and S, J. Lie Theory 17 (2007), no. 3, 449-468.

7.
W.-D. Liu and Y.-H. He, Finite-dimensional special odd Hamiltonian superalgebras in prime characteristic, Commun. Contemp. Math. 11 (2009), no. 4, 523-546. crossref(new window)

8.
W.-D. Liu, X.-Y. Hua, and Y.-C. Su, Derivations of the even part of the odd Hamiltonian superalgebra in modular case, Acta Math Sin. 25 (2009), no. 3, 355-378.

9.
W.-D. Liu and Y.-Z. Zhang, Outer derivation algebras of finite-dimensional Cartan-type modular Lie superalgebras, Comm. Algebra 33 (2005), no. 7, 2131-2214. crossref(new window)

10.
W.-D. Liu, Derivations of the even parts for modular Lie superalgebras of Cartan type W and S, Internat. J. Algebra Comput. 17 (2007), no. 4, 661-714. crossref(new window)

11.
W.-D. Liu, Y.-Z. Zhang, and X.-L. Wang, The derivation algebra of the Cartan-type Lie superalgebra HO, J. Algebra 273 (2004), no. 1, 176-205. crossref(new window)

12.
H. Strade, Simple Lie algebras over fields of positive characteristic. I, Structure Theory, Walter de Gruyter, Berlin and New York, 2004.

13.
H. Strade and R. Farnsteiner, Modular Lie Algebras and Their Representations, Monographs and Texbooks in Pure and Appl. Math. Vol. 116. Marcel Dekker Inc. 1988.

14.
W.-Q. Wang and L. Zhao, Representations of Lie superalgebras in prime characteristic I, arXiv: 0808.0046v[math.RT], 12 Jan 2009.

15.
C.-W. Zhang, Simple modules for the restricted Lie superalgebras sl(n, 1), J. Pure Appl. Algebra 213 (2009), no. 5, 756-765. crossref(new window)

16.
Y.-Z. Zhang, Finite-dimensional Lie superalgebras of Cartan type over fields of prime characteristic, Chinese Sci. Bull. 42 (1997), no. 9, 720-724. crossref(new window)

17.
Y.-Z. Zhang, Graded modules for Z-graded Lie superalgebras W(n) and S(n) of Cartan type, Kexue Tongbao (Chinese) 40 (1995), no. 20, 1829-1832.

18.
Y.-Z. Zhang, Z-graded module of Lie superalgebra H(n) of Cartan type, Chinese Sci. Bull. 41 (1996), no. 10, 813-817.