Strong homotopy Lie algebras, homotopy Poisson manifolds and Courant algebroids

doi:http://dx.doi.org/10.1007/s11005-016-0925-8

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	Strong homotopy Lie algebras, homotopy Poisson manifolds and Courant algebroids
	Xu, XM; Lang, HL; Sheng, YH; Sheng, YH (reprint author), Jilin Univ, Dept Math, Changchun 130012, Peoples R China.; Sheng, YH (reprint author), Chinese Acad Sci, Kavli Inst Theoret Phys China, Beijing 100190, Peoples R China.
刊名	LETTERS IN MATHEMATICAL PHYSICS
	2017
卷号	107 期号:5 页码:861-885
关键词	L-infinity-algebras Lie 2-algebras Homotopy Poisson Manifolds Courant Algebroids Symplectic Nq-manifolds Maurer-cartan Elements
DOI	http://dx.doi.org/10.1007/s11005-016-0925-8
英文摘要	We study Maurer-Cartan elements on homotopy Poisson manifolds of degree n. They unify many twisted or homotopy structures in Poisson geometry and mathematical physics, such as twisted Poisson manifolds, quasi-Poisson -manifolds, and twisted Courant algebroids. Using the fact that the dual of an n-term -algebra is a homotopy Poisson manifold of degree , we obtain a Courant algebroid from a 2-term -algebra via the degree 2 symplectic NQ-manifold . By integrating the Lie quasi-bialgebroid associated to the Courant algebroid, we obtain a Lie-quasi-Poisson groupoid from a 2-term -algebra, which is proposed to be the geometric structure on the dual of a Lie 2-algebra. These results lead to a construction of a new 2-term -algebra from a given one, which could produce many interesting examples.
学科主题	Physics
语种	英语
内容类型	期刊论文
源URL	[http://ir.itp.ac.cn/handle/311006/22070]
专题	理论物理研究所_理论物理所1978-2010年知识产出
通讯作者	Sheng, YH (reprint author), Jilin Univ, Dept Math, Changchun 130012, Peoples R China.; Sheng, YH (reprint author), Chinese Acad Sci, Kavli Inst Theoret Phys China, Beijing 100190, Peoples R China.
推荐引用方式 GB/T 7714	Xu, XM,Lang, HL,Sheng, YH,et al. Strong homotopy Lie algebras, homotopy Poisson manifolds and Courant algebroids[J]. LETTERS IN MATHEMATICAL PHYSICS,2017,107(5):861-885.
APA	Xu, XM,Lang, HL,Sheng, YH,Sheng, YH ,&Sheng, YH .(2017).Strong homotopy Lie algebras, homotopy Poisson manifolds and Courant algebroids.LETTERS IN MATHEMATICAL PHYSICS,107(5),861-885.
MLA	Xu, XM,et al."Strong homotopy Lie algebras, homotopy Poisson manifolds and Courant algebroids".LETTERS IN MATHEMATICAL PHYSICS 107.5(2017):861-885.