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Strong homotopy Lie algebras, homotopy Poisson manifolds and Courant algebroids
Lang, HL; Sheng, YH; Xu, XM; 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.
2017
发表期刊LETTERS IN MATHEMATICAL PHYSICS
卷号107期号:5页码:861-885
文章类型Article
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.
关键词L-infinity-algebras Lie 2-algebras Homotopy Poisson Manifolds Courant Algebroids Symplectic Nq-manifolds Maurer-cartan Elements
学科领域Physics
资助者NSFC [11101179, 11471139] ; NSFC [11101179, 11471139] ; NSFC [11101179, 11471139] ; NSFC [11101179, 11471139] ; NSF of Jilin Province [20140520054JH] ; NSF of Jilin Province [20140520054JH] ; NSF of Jilin Province [20140520054JH] ; NSF of Jilin Province [20140520054JH] ; SNSF [P2GEP2-165118] ; SNSF [P2GEP2-165118] ; SNSF [P2GEP2-165118] ; SNSF [P2GEP2-165118] ; NCCR SwissMAP ; NCCR SwissMAP ; NCCR SwissMAP ; NCCR SwissMAP ; NSFC [11101179, 11471139] ; NSFC [11101179, 11471139] ; NSFC [11101179, 11471139] ; NSFC [11101179, 11471139] ; NSF of Jilin Province [20140520054JH] ; NSF of Jilin Province [20140520054JH] ; NSF of Jilin Province [20140520054JH] ; NSF of Jilin Province [20140520054JH] ; SNSF [P2GEP2-165118] ; SNSF [P2GEP2-165118] ; SNSF [P2GEP2-165118] ; SNSF [P2GEP2-165118] ; NCCR SwissMAP ; NCCR SwissMAP ; NCCR SwissMAP ; NCCR SwissMAP
DOIhttp://dx.doi.org/10.1007/s11005-016-0925-8
关键词[WOS]BIALGEBROIDS ; GEOMETRY ; QUASI ; REDUCTION ; BRACKETS
语种英语
资助者NSFC [11101179, 11471139] ; NSFC [11101179, 11471139] ; NSFC [11101179, 11471139] ; NSFC [11101179, 11471139] ; NSF of Jilin Province [20140520054JH] ; NSF of Jilin Province [20140520054JH] ; NSF of Jilin Province [20140520054JH] ; NSF of Jilin Province [20140520054JH] ; SNSF [P2GEP2-165118] ; SNSF [P2GEP2-165118] ; SNSF [P2GEP2-165118] ; SNSF [P2GEP2-165118] ; NCCR SwissMAP ; NCCR SwissMAP ; NCCR SwissMAP ; NCCR SwissMAP ; NSFC [11101179, 11471139] ; NSFC [11101179, 11471139] ; NSFC [11101179, 11471139] ; NSFC [11101179, 11471139] ; NSF of Jilin Province [20140520054JH] ; NSF of Jilin Province [20140520054JH] ; NSF of Jilin Province [20140520054JH] ; NSF of Jilin Province [20140520054JH] ; SNSF [P2GEP2-165118] ; SNSF [P2GEP2-165118] ; SNSF [P2GEP2-165118] ; SNSF [P2GEP2-165118] ; NCCR SwissMAP ; NCCR SwissMAP ; NCCR SwissMAP ; NCCR SwissMAP
WOS类目Physics, Mathematical
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文献类型期刊论文
条目标识符http://ir.itp.ac.cn/handle/311006/22070
专题理论物理所SCI论文
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
Lang, HL,Sheng, YH,Xu, XM,et al. Strong homotopy Lie algebras, homotopy Poisson manifolds and Courant algebroids[J]. LETTERS IN MATHEMATICAL PHYSICS,2017,107(5):861-885.
APA Lang, HL,Sheng, YH,Xu, XM,Sheng, YH ,&Sheng, YH .(2017).Strong homotopy Lie algebras, homotopy Poisson manifolds and Courant algebroids.LETTERS IN MATHEMATICAL PHYSICS,107(5),861-885.
MLA Lang, HL,et al."Strong homotopy Lie algebras, homotopy Poisson manifolds and Courant algebroids".LETTERS IN MATHEMATICAL PHYSICS 107.5(2017):861-885.
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