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	DIRAC STRUCTURES OF OMNI-LIE ALGEBROIDS
	Chen, Zhuo ; Liu, Zhang Ju ; Sheng, Yunhe
	2011
关键词	Omni-Lie algebroid Dirac structures local Lie algebras reduction normalizer deformation GENERALIZED COMPLEX STRUCTURES MOMENT MAPS REDUCTION MANIFOLDS
英文摘要	Omni-Lie algebroids are generalizations of Alan Weinstein's omni-Lie algebras. A Dirac structure in an omni-Lie algebroid DE circle plus JE is necessarily a Lie algebroid together with a representation on E. We study the geometry underlying these Dirac structures in the light of reduction theory. In particular, we prove that there is a one-to-one correspondence between reducible Dirac structures and projective Lie algebroids in T = TM circle plus E; we establish the relation between the normalizer N(L) of a reducible Dirac structure L and the derivation algebra Der(b(L)) of the projective Lie algebroid b(L); we study the cohomology group H(center dot)(L, rho(L)) and the relation between N(L) and H(1)(L, rho(L)); we describe Lie bialgebroids using the adjoint representation; we study the deformation of a Dirac structure L, which is related with H(2)(L, rho(L)).; Mathematics; SCI(E); 1; ARTICLE; 8; 1163-1185; 22
语种	英语
出处	SCI
出版者	international journal of mathematics
内容类型	其他
源URL	[http://hdl.handle.net/20.500.11897/394437]
专题	数学科学学院
推荐引用方式 GB/T 7714	Chen, Zhuo,Liu, Zhang Ju,Sheng, Yunhe. DIRAC STRUCTURES OF OMNI-LIE ALGEBROIDS. 2011-01-01.

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