Abstract
Poisson structures related to affine Courant-type algebroids are analyzed, including those related with cotangent bundles on Lie-group manifolds. Special attention is paid to Courant-type algebroids and their related R structures generated by suitably defined tensor mappings. Lie–Poisson brackets that are invariant with respect to the coadjoint action of the loop diffeomorphism group are created, and the related Courant-type algebroids are described. The corresponding integrable Hamiltonian flows generated by Casimir functionals and generalizing so-called heavenly-type differential systems describing diverse geometric structures of conformal type in finite dimensional Riemannian manifolds are described.
Original language | English |
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Article number | 76 |
Journal | Symmetry |
Volume | 16 |
Issue number | 1 |
DOIs | |
Publication status | Published - Jan 2024 |
Keywords
- Courant algebroid
- Grassmann algebra
- Hamiltonian systems
- Lie algebroid
- Poisson structure
- coadjoint orbits
- differentiation
- integrability
- invariants
ASJC Scopus subject areas
- Computer Science (miscellaneous)
- Chemistry (miscellaneous)
- General Mathematics
- Physics and Astronomy (miscellaneous)