The existence and classification of couplings between Lie algebroids and tangent bundlesстатья
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Аннотация:In this paper we investigate the existence and classification of couplings betweenLie algebra bundles and tangent bundles. We first give a sufficient and necessarycondition on the existence of coupling between Lie algebra bundle (LAB) andthe tangent bundle; i.e., we define a new topology on the group Aut g of allautomorphisms of the Lie algebra g, denoted by Aut g^δ, and show that the tangentbundle TM can be coupled with the Lie algebra bundle L if and only if L admits alocal trivial structure with structural group endowed with such new topology. Thenwe show that there is a bijection between Coup_g(M) the set of all isomorphismclasses of couplings (L, Ξ) and the set LAB^δ_g(M) of isomorphism classes of g-bundleswith structural group Aut g^δ.