Notions of quasi-Jacobi bialgebroid and its Dirac-Jacobi structure are introduced.The necessary and sufficient conditions for a maximal isotropic subbundle L to be a DiracJacobi structure are proved.Meanwhile several ...Notions of quasi-Jacobi bialgebroid and its Dirac-Jacobi structure are introduced.The necessary and sufficient conditions for a maximal isotropic subbundle L to be a DiracJacobi structure are proved.Meanwhile several special examples are presented.展开更多
Protobialgebroids include several kinds of algebroid structures such as Lie algebroid,Lie bialgebroid, Lie quasi-bialgebroid, etc. In this paper, the Dirac theories are generalized from Lie bialgebroid to protobialgeb...Protobialgebroids include several kinds of algebroid structures such as Lie algebroid,Lie bialgebroid, Lie quasi-bialgebroid, etc. In this paper, the Dirac theories are generalized from Lie bialgebroid to protobialgebroid. We give the integrable conditions for a maximally isotropic subbundle being a Dirac structure for a protobialgebroid by the notion of a characteristic pair. From the integrable conditions, we found out that the Dirac structure has closed relations with the twisting of a protobialgebroid. At last, some special cases of the Dirac structures for protobialgebroids are discussed.展开更多
基金Supported by the Scientific Reseaxch Common Program of Beijing Municipal Commission of Education(SQKM201211232017)Supported by the Beijing Excellent Training Grant(2012D005007000005)Supported by the Funding Program for Academic Human Resources Development in Institutions of Higher Learning Under the Jurisdiction of Beijing Municipality(11530500015)
文摘Notions of quasi-Jacobi bialgebroid and its Dirac-Jacobi structure are introduced.The necessary and sufficient conditions for a maximal isotropic subbundle L to be a DiracJacobi structure are proved.Meanwhile several special examples are presented.
文摘Protobialgebroids include several kinds of algebroid structures such as Lie algebroid,Lie bialgebroid, Lie quasi-bialgebroid, etc. In this paper, the Dirac theories are generalized from Lie bialgebroid to protobialgebroid. We give the integrable conditions for a maximally isotropic subbundle being a Dirac structure for a protobialgebroid by the notion of a characteristic pair. From the integrable conditions, we found out that the Dirac structure has closed relations with the twisting of a protobialgebroid. At last, some special cases of the Dirac structures for protobialgebroids are discussed.
