Open AccessHolonomy transformations for Lie subalgebroids
Author(s) -
Marco Zambon
Publication year - 2021
Publication title -
journal of geometric mechanics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.511
H-Index - 17
eISSN - 1941-4897
pISSN - 1941-4889
DOI - 10.3934/jgm.2021016
Subject(s) - holonomy , connection (principal bundle) , mathematics , pure mathematics , action (physics) , lie algebra , foliation (geology) , algebra over a field , geometry , physics , geology , quantum mechanics , geochemistry , metamorphic rock
Given a foliation, there is a well-known notion of holonomy, which can be understood as an action that differentiates to the Bott connection on the normal bundle. We present an analogous notion for Lie subalgebroids, consisting of an effective action of the minimal integration of the Lie subalgebroid, and provide an explicit description in terms of conjugation by bisections. The construction is done in such a way that it easily extends to singular subalgebroids, which provide our main motivation.