Banach-Lie groupoids and generalized inversion

Abstract

We study a few basic properties of Banach-Lie groupoids and algebroids, adapting some classical results on finite dimensional Lie groupoids. As an illustration of the general theory, we show that the notion of locally transitive Banach-Lie groupoid sheds fresh light on earlier research on some infinite-dimensional manifolds associated with Banach algebras.

45 pages, too appear in J. Funct. Anal

References in corpus (7)

• Lectures on Integrability of Lie Brackets
• The Lie group of bisections of a Lie groupoid
• Almost Lie structures on an anchored Banach bundle
• Fundamentals of submersions and immersions between infinite-dimensional manifolds
• (Re)constructing Lie groupoids from their bisections and applications to prequantisation
• Algebroids associated to the groupoid of partially invertible elements of a $W^{\ast }$-algebra
• Groupoids and inverse semigroups associated to W*-algebras

Cited by in corpus (1)

• Convenient Partial Poisson Manifolds