Covariant Lie derivatives and Fr\"olicher-Nijenhuis bracket on Lie Algebroids
Antonio De Nicola, Ivan Yudin
TL;DR
This paper introduces covariant Lie derivatives on Lie algebroids, enabling a concise formula for the Fr"olicher-Nijenhuis bracket, advancing the understanding of geometric structures on Lie algebroids.
Contribution
It defines covariant Lie derivatives on vector-valued forms for Lie algebroids and derives a simplified formula for the Fr"olicher-Nijenhuis bracket.
Findings
Covariant Lie derivatives are well-defined on Lie algebroids.
A concise formula for the Fr"olicher-Nijenhuis bracket is obtained.
The results enhance the geometric analysis on Lie algebroids.
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 Fr\"olicher-Nijenhuis bracket on Lie algebroids.
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