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Scientific Article
unige:12225 
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Lie theory and the Chern-Weil homomorphism |
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| Authors | ||
| Published in | Annales scientifiques de l'Ecole normale supérieure. 2005, vol. 38, no. 2, p. 303-338 | |
| 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. | |
| Stable URL | https://archive-ouverte.unige.ch/unige:12225 | |
| Full text | ||
| Identifiers |
arXiv: math/0308135v1 |
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| Structures |
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