On Some Aspects of the Courant-Type Algebroids, the Related Coadjoint Orbits and Integrable Systems

Anatolij K. Prykarpatski, Victor A. Bovdi

Research output: Contribution to journalArticlepeer-review

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 languageEnglish
Article number76
JournalSymmetry
Volume16
Issue number1
DOIs
Publication statusPublished - 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)

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