Strongly Homotopy Lie Bialgebras and Lie Quasi-bialgebras |
| |
Authors: | Olga Kravchenko |
| |
Institution: | (1) Université de Lyon, Université Lyon 1, CNRS, UMR 5208 Institut Camille Jordan, 69622 Villeurbanne Cedex, France |
| |
Abstract: | Structures of Lie algebras, Lie coalgebras, Lie bialgebras and Lie quasibialgebras are presented as solutions of Maurer–Cartan
equations on corresponding governing differential graded Lie algebras using the big bracket construction of Kosmann–Schwarzbach.
This approach provides a definition of an L
∞-(quasi)bialgebra (strongly homotopy Lie (quasi)bialgebra). We recover an L
∞-algebra structure as a particular case of our construction. The formal geometry interpretation leads to a definition of an
L
∞ (quasi)bialgebra structure on V as a differential operator Q on V, self-commuting with respect to the big bracket. Finally, we establish an L
∞-version of a Manin (quasi) triple and get a correspondence theorem with L
∞-(quasi)bialgebras.
This paper is dedicated to Jean-Louis Loday on the occasion of his 60th birthday with admiration and gratitude. |
| |
Keywords: | 17B62 (58A50 18G55) |
本文献已被 SpringerLink 等数据库收录! |
|