1. Left-symmetric bialgebroids and their corresponding Manin triples.
- Author
-
Liu, Jiefeng, Sheng, Yunhe, and Bai, Chengming
- Subjects
- *
LIE algebras , *DIFFERENTIAL geometry , *MATHEMATICS , *GENERALIZATION , *ALGEBROIDS - Abstract
In this paper, we introduce the notion of a left-symmetric bialgebroid as a geometric generalization of a left-symmetric bialgebra and construct a left-symmetric bialgebroid from a pseudo-Hessian manifold. We also introduce the notion of a Manin triple for left-symmetric algebroids, which is equivalent to a left-symmetric bialgebroid. The corresponding double structure is a pre-symplectic algebroid rather than a left-symmetric algebroid. In particular, we establish a relation between Maurer–Cartan type equations and Dirac structures of the pre-symplectic algebroid which is the corresponding double structure for a left-symmetric bialgebroid. [ABSTRACT FROM AUTHOR]
- Published
- 2018
- Full Text
- View/download PDF