Extended Curvatures and Lie Algebroids

Abstract

The aim of the paper is to find conditions in which the derived almost Lie vector bundle E1 of an almost Lie vector bundle E is a Lie algebroid. The conditions are that some extended curvatures on E, considered in the paper, are vanishing. Two non-trivial examples are given. One example is when E0 is a skew symmetric algebroid; the other one is when E1 is not a skew symmetric algebroid.

Keywords

• almost Lie vector bundle
• skew symmetric algebroid
• Jacobiator
• Lie algebroid