Covariant Lie derivatives and Frölicher–Nijenhuis bracket on Lie algebroids

2014/12/08 by Antonio De Nicola, Ivan Yudin
Mathematics · Physics and Astronomy · #Adjoint representation #Algebraic structures and combinatorial models #Bracket #Covariant transformation #Homotopy and Cohomology in Algebraic Topology #Lie algebra #Lie algebroid #Lie bracket of vector fields #Lie group #Nonlinear Waves and Solitons #Simple Lie group #math.DG

paper · pdf · doi:10.1142/s021988781560018x

published as Int. J. Geom. Methods Mod. Phys. 12 (2015), no. 9, 1560018 (8 pages) · 6 pages

arxiv created 2014/12/08 · openalex publication_date 2015/07/15 · arxiv updated 2015/10/14 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

We define covariant Lie derivatives acting on vector-valued forms on Lie algebroids and study their properties. This allows us to obtain a concise formula for the Frölicher–Nijenhuis bracket on Lie algebroids.

Citations

• Lie algebroids and Poisson-Nijenhuis structures
• Complex Analytic Coordinates in Almost Complex Manifolds
• Theory of Vector-Valued Differential Forms