Lie theory and the Chern-Weil homomorphism

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dc.creatorAlekseev, A.
dc.creatorMeinrenken, E.
dc.date2003-08-14
dc.date.accessioned2026-07-07T10:12:44Z
dc.date.available2026-07-07T10:12:44Z
dc.descriptionWe introduce a canonical Chern-Weil map for possibly non-commutative g-differential algebras with connection. Our main observation is that the generalized Chern-Weil map is an algebra homomorphism ``up to g-homotopy''. Hence, the induced map from invariant polynomials to the basic cohomology is an algebra homomorphism. As in the standard Chern-Weil theory, this map is independent of the choice of connection. Applications of our results include: a conceptually easy proof of the Duflo theorem for quadratic Lie algebras, a short proof of a conjecture of Vogan on Dirac cohomology, generalized Harish-Chandra projections for quadratic Lie algebras, an extension of Rouviere's theorem for symmetric pairs, and a new construction of universal characteristic forms in the Bott-Shulman complex.
dc.description38 pages
dc.identifierhttps://arxiv.org/abs/math/0308135
dc.identifierhttp://arxiv.org/abs/math/0308135
dc.identifierAnn. Sci. Ecole Norm. Sup. (4) 38 (2005), no. 2, 303--338
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/172283
dc.subjectRepresentation Theory
dc.titleLie theory and the Chern-Weil homomorphism
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