SUPERSYMMETRIC INVARIANCE AND UNIVERSAL CENTRAL EXTENSIONS OF LIE SUPERTRIPLE SYSTEMS

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

Acta mathematica scientia,Series B ›› 2014, Vol. 34 ›› Issue (2): 313-330.doi: 10.1016/S0252-9602(14)60007-2

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SUPERSYMMETRIC INVARIANCE AND UNIVERSAL CENTRAL EXTENSIONS OF LIE SUPERTRIPLE SYSTEMS

|ZHANG Qing-Cheng, WEI Zhu*, CHU Ying-Na, ZHANG Yong-Ping

School of Mathematics and Statistics, Northeast Normal University, Changchun 130024, China； Department of Mathematics, Shenyang Institute of Chemical Technology, Shenyang 110142, China

Received:2011-11-22 Revised:2013-06-18 Online:2014-03-20 Published:2014-03-20
Contact: WEI Zhu，weiz986@nenu.edu.cn E-mail:zhangqc569@nenu.edu.cn; weiz986@nenu.edu.cn；zhangyongping78@163.com
Supported by:
The first author is supported by the NSFC (10871057), and NSFJL (20130101068JC). The second author is supported by Fundamental Research Funds for the Central Universities of China and SRFHLJED (12521157).

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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SUPERSYMMETRIC INVARIANCE AND UNIVERSAL CENTRAL EXTENSIONS OF LIE SUPERTRIPLE SYSTEMS

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