Local and global integrability of Lie brackets

DOI10.3934/jgm.2021024zbMath1505.58005arXiv2104.07756OpenAlexW3199437835MaRDI QIDQ2065148

Yuxuan Zhang, Rui Loja Fernandes

Publication date: 7 January 2022

Published in: Journal of Geometric Mechanics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2104.07756

zbMATH Keywords

local and global integrabilityassociativitymultiplicative forminfinitesimal multiplicative formlocal groupoid

Mathematics Subject Classification ID

Topological groupoids (including differentiable and Lie groupoids) (22A22) Pseudogroups and differentiable groupoids (58H05)

Cites Work

• The role of the Jacobi identity in solving the Maurer-Cartan structure equation
• Multiplicative Dirac structures
• Multiplicative forms at the infinitesimal level
• Integration of twisted Poisson structures
• Integration of holomorphic Lie algebroids
• Foliated groupoids and infinitesimal ideal systems
• Linear and multiplicative 2-forms
• Integrability of Lie brackets
• Differential forms with values in VB-groupoids and its Morita invariance
• Integrability of Poisson brackets
• Lie algebroids, holonomy and characteristic classes
• Integration of twisted Dirac brackets
• Integration of Lie bialgebroids
• On local integration of Lie brackets
• Lie theory of multiplicative tensors
• Multiplicative forms and Spencer operators
• Universal lifting theorem and quasi-Poisson groupoids
• Symplectic groupoids and Poisson manifolds
• Associativity and integrability
• Local analytic geometry of generalized complex structures
• The classifying Lie algebroid of a geometric structure I: Classes of coframes
• Lie groups
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