Lie theory of multiplicative tensors
arXiv:1705.08579 · doi:10.1007/s00208-019-01881-w
Abstract
We study tensors on Lie groupoids suitably compatible with the groupoid structure, called {\em multiplicative}. Our main result gives a complete description of these objects only in terms of infinitesimal data. Special cases include the infinitesimal counterparts of multiplicative forms, multivector fields and holomorphic structures, obtained through a unifying and conceptual method. We also give a full treatment of multiplicative vector-valued forms, particularly Nijenhuis operators and related structures.
arXiv comment54 pages. v2: minor corrections, typos fixed, references updated
References in corpus (18)
- Higher vector bundles and multi-graded symplectic manifolds
- Lie algebroids and Poisson-Nijenhuis structures
- Holomorphic Poisson Manifolds and Holomorphic Lie Algebroids
- Poisson sigma models and symplectic groupoids
- Vector bundles over Lie groupoids and algebroids
- Linear and multiplicative 2-forms
- Poisson Quasi-Nijenhuis Manifolds
- Quasi-Hamiltonian groupoids and multiplicative Manin pairs
- Integration of Holomorphic Lie Algebroids
- Integration of twisted Poisson structures
- VB-algebroid morphisms and representations up to homotopy
- Differential forms with values in VB-groupoids
- Poisson 2-groups
- Infinitesimal Automorphisms of VB-groupoids and algebroids
- Multiplicative Dirac structures
- Lie groupoids and the Frolicher-Nijenhuis bracket
- Glanon groupoids
- Multiplicative integrable models from Poisson-Nijenhuis structures
Cited by in corpus (17)
- Differential forms with values in VB-groupoids
- Infinitesimal Automorphisms of VB-groupoids and algebroids
- Dirac structures and Nijenhuis operators
- On the prequantisation map for 2-plectic manifolds
- Lie-Nijenhuis bialgebroids
- Local formulas for multiplicative forms
- Integrability of quotients in Poisson and Dirac geometry
- Multiplicative Connections and Their Lie Theory
- Fiber-Wise Linear Differential Operators
- Quasi-Lie bialgebroids, Dirac structures and deformations of Poisson quasi-Nijenhuis manifolds
- Integrating Nijenhuis Structures
- On the reduced space of multiplicative multivectors
- Linear generalised complex structures
- Courant-Nijenhuis algebroids
- Higher Vector Bundles
- Poisson-Nijenhuis Structure on Lie groupoids from the Invariance's Point of View
- Affine structures on Lie groupoids