SUPERSYMMETRIC INVARIANCE AND UNIVERSAL CENTRAL EXTENSIONS OF LIE SUPERTRIPLE SYSTEMS

doi:10.1016/S0252-9602(14)60007-2

Abstract

Abstract:

In this article, we discuss some properties of a supersymmetric invariant bilinear form on Lie supertriple systems. In particular, a supersymmetric invariant bilinear form on Lie supertriple systems can be extended to its standard imbedding Lie superalgebras. Furthermore, we generalize Garland´s theory of universal central extensions for Lie supertriple systems following the classical one for Lie superalgebras. We solve the problems of lifting automorphisms and lifting derivations.

Key words: Supersymmetric invariant bilinear form, Lie supertriple system, central exten-sion, automorphism, derivation

CLC Number:

17B05

ZHANG Qing-Cheng, WEI Zhu, CHU Ying-Na, ZHANG Yong-Ping. SUPERSYMMETRIC INVARIANCE AND UNIVERSAL CENTRAL EXTENSIONS OF LIE SUPERTRIPLE SYSTEMS[J].Acta mathematica scientia,Series B, 2014, 34(2): 313-330.

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