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Maurer-Cartan characterizations and cohomologies of compatible Lie algebras.
- Source :
- SCIENCE CHINA Mathematics; Jun2023, Vol. 66 Issue 6, p1177-1198, 22p
- Publication Year :
- 2023
-
Abstract
- In this paper, we give Maurer-Cartan characterizations as well as a cohomology theory for compatible Lie algebras. Explicitly, we first introduce the notion of a bidifferential graded Lie algebra and thus give Maurer-Cartan characterizations of compatible Lie algebras. Then we introduce a cohomology theory of compatible Lie algebras and use it to classify infinitesimal deformations and abelian extensions of compatible Lie algebras. In particular, we introduce the reduced cohomology of a compatible Lie algebra and establish the relation between the reduced cohomology of a compatible Lie algebra and the cohomology of the corresponding compatible linear Poisson structures introduced by Dubrovin and Zhang (2001) in their study of bi-Hamiltonian structures. Finally, we use the Maurer-Cartan approach to classify nonabelian extensions of compatible Lie algebras. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 16747283
- Volume :
- 66
- Issue :
- 6
- Database :
- Complementary Index
- Journal :
- SCIENCE CHINA Mathematics
- Publication Type :
- Academic Journal
- Accession number :
- 164005778
- Full Text :
- https://doi.org/10.1007/s11425-021-2014-5