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Duality for base-changing morphisms of vector bundles, modules, Lie algebroids and Poisson structures

Published online by Cambridge University Press:  24 October 2008

Philip J. Higgins
Affiliation:
Department of Mathematical Sciences, University of Durham, Durham DH1 3LE
Kirill C. H. Mackenzie
Affiliation:
Department of Pure Mathematics, University of Sheffield, Sheffield S3 7RH

Abstract

The main result of this paper is an extension to Poisson bundles [4] and Lie algebroids of the classical result that a linear map of Lie algebras is a morphism of Lie algebras if and only if its dual is a Poisson morphism. In formulating this extension we introduce a second class of structural maps for vector bundles, which we call comorphisms, alongside the standard morphisms, and we further show that this concept of comorphism, in conjunction with a corresponding concept for modules, allows one to extend to arbitrary base-changing morphisms of arbitrary vector bundles the familiar duality and section functors which are normally denned only in the base-preserving case.

Type
Research Article
Copyright
Copyright © Cambridge Philosophical Society 1993

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