Poisson structures on the cotangent bundle of a Lie group or a principle bundle and their reductions

DOI10.1063/1.530822zbMath0822.58016arXivmath/9312213OpenAlexW2119957637WikidataQ115329901 ScholiaQ115329901MaRDI QIDQ4327218

Peter W. Michor, Janusz Grabowski, Dimitrii V. Alekseevsky, Giuseppe Marmo

Publication date: 5 April 1995

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/9312213

zbMATH Keywords

cotangent bundlePoisson structureLie groupprinciple bundle

Mathematics Subject Classification ID

Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems (37J99) Lie algebras of Lie groups (22E60)

Related Items

Hamiltonian dynamics on matched pairs, Lagrangian dynamics on matched pairs, Poisson structures on almost complex Lie algebroids, Some notes on lifts of the F((υ+1),λ²(υ-1))-structure on cotangent and tangent bundle, Tulczyjew’s triplet for lie groups III: Higher order dynamics and reductions for iterated bundles, Classical dynamics, alternative carrier spaces and group-valued constants of motion, Poisson structures on double Lie groups, SOME HIGHLIGHTS OF DMITRY ALEKSEEVSKY'S WORK, Born sigma-models for para-Hermitian manifolds and generalized T-duality, HOLOMORPHIC SYMPLECTIC AND POISSON STRUCTURES ON THE HOLOMORPHIC COTANGENT BUNDLE OF A COMPLEX LIE GROUP AND OF A HOLOMORPHIC PRINCIPAL BUNDLE

Cites Work

• Canonical formulations of a classical particle in a Yang-Mills field and Wong's equations
• A universal phase space for particles in Yang-Mills fields
• Gauged Lie-Poisson structures
• Minimal coupling and the symplectic mechanics of a classical particle in the presence of a Yang-Mills field