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Lie theory and the Chern-Weil homomorphism | | A. Alekseev
; E. Meinrenken
; | | Date: |
14 Aug 2003 | | Subject: | Representation Theory | math.RT | | Abstract: | We 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. | | Source: | arXiv, math.RT/0308135 | | Services: | Forum | Review | PDF | Favorites | |
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