Lie-Rinehart algebras, descent, and quantization

2003/03/02 by Johannes Huebschmann · 1 citation
Mathematics · Physics and Astronomy · #math.SG #math-ph #math.MP #msc:14L24 #msc:14L30 #msc:17B63 #msc:17B65 #msc:17B66 #msc:17B81 #msc:31C17 #msc:32C20 #msc:32Q15 #msc:32S05 #msc:32S60 #msc:53D17 #msc:53D20 #msc:53D50 #msc:58F05 #msc:58F06 #msc:81S10

paper · pdf

published as In: Galois theory, Hopf algebras, and semiabelian categories, Fields Inst. Commun. 43 (2004), 295-316 · AMSTeX 2.1, 23 pages

arxiv created 2003/03/02 · arxiv updated 2009/11/30

Abstract

A Lie-Rinehart algebra consists of a commutative algebra and a Lie algebra with additional structure which generalizes the mutual structure of interaction between the algebra of functions and the Lie algebra of smooth vector fields on a smooth manifold. Lie-Rinehart algebras provide the correct categorical language to solve the problem whether Kaehler quantization commutes with reduction which, in turn, may be seen as a descent problem.

Cited by

• On longitudinal differential operators and Nash blowups

Related

• Lie algebroids. Lie-Rinehart algebras
• A Lie-Rinehart algebra with no antipode
• Lie Infinity-Algebras from Lie Rinehart Pairs
• The universal Hopf algebra associated with a Hopf-Lie-Rinehart algebra
• Universal enveloping algebras of Lie-Rinehart algebras: crossed products, connections, and curvature