Journal of the
Korean Mathematical Society
JKMS

ISSN(Print) 0304-9914 ISSN(Online) 2234-3008

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J. Korean Math. Soc. 2013; 50(3): 591-605

Printed May 1, 2013

https://doi.org/10.4134/JKMS.2013.50.3.591

Copyright © The Korean Mathematical Society.

Derivations of the odd contact Lie algebras in prime characteristic

Yan Cao, Xiumei Sun, and Jixia Yuan

Harbin University of Science and Technology, Harbin Normal University, Heilongjiang University

Abstract

The underlying field is of characteristic $p>2$. 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

MSC numbers: 17B50, 17B40