Anchored vector bundles and Lie algebroids
Volume 54 / 2001
Banach Center Publications 54 (2001), 51-69
MSC: 18F15, 55R25, 22A30, 18B40, 58H99.
DOI: 10.4064/bc54-0-5
Abstract
The derived generalized algebroid and the derived generalized Lie algebroid of an anchored vector bundle are defined. Some natural functors from the two categories of anchored vector bundles to the corresponding categories of generalized algebroids and generalized Lie algebroids respectively are also considered.
A natural result is proved: the derived (Lie) algebroid of an anchored vector subbundle is a generalized (Lie) algebroid of the underlying bundle. Lifts of linear R-connections and skew-symmetric forms respectively are constructed and the modular class of an almost Lie structure is defined.
