Brackets

Abstract

We review origins and main properties of the most important bracket operations appearing canonically in differential geometry and mathematical physics in the classical, as well as the supergeometric setting. The review is supplemented by a few new concepts and examples.

40 pages, minor corrections, to appear in IJGMMP

References in corpus (6)

• n-ary algebras: a review with applications
• Generalized complex geometry
• Tangent Lifts of Poisson and Related Structures
• Coisotropic deformations of associative algebras and dispersionless integrable hierarchies
• On higher analogues of Courant algebroids
• On the Geometry of Multi-Dirac Structures and Gerstenhaber Algebras

Cited by in corpus (19)

• Covariant-differential formulation of Lagrangian field theory
• A novel approach to contact Hamiltonians and contact Hamilton-Jacobi theory
• On the Strong Homotopy Lie-Rinehart Algebra of a Foliation
• Higher order mechanics on graded bundles
• Almost Lie Algebroids and Characteristic Classes
• Reductions: precontact versus presymplectic
• Contact Lie systems
• Differential Calculus on Manifolds with a Boundary. Applications
• VB-structures and generalizations
• Dispersionless (3+1)-dimensional integrable hierarchies
• Geometry of Lagrangian and Hamiltonian formalisms in the dynamics of strings
• Symmetries and Reduction -- part I -- Poisson and symplectic picture
• Liouville-Arnold theorem for homogeneous symplectic and contact Hamiltonian systems
• On Computational Poisson Geometry II: Numerical Methods
• Omni $n$-Lie algebras and linearization of higher analogues of Courant algebroids
• Jacobi algebroids and Jacobi sigma models
• Lie algebroids generated by cohomology operators
• Remarks on generalized Lie algebroids and related concepts
• Mixed superposition rules for Lie systems, compatible geometric structures, and applications