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Transgression and Clifford algebras

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Published in Annales de l'Institut Fourier. 2009, vol. 59, no. 4, p. 1337-1358
Abstract Let $W$ be a differential (not necessarily commutative) algebra which carries a free action of a polynomial algebra $SP$ with homogeneous generators $p_1, >..., p_r$. We show that for $W$ acyclic, the cohomology of the quotient $H(W/<p_1,..., p_r>)$ is isomorphic to a Clifford algebra $ ext{Cl}(P,B)$, where the (possibly degenerate) bilinear form $B$ depends on $W$. This observation is an analogue of an old result of Borel in a non-commutative context. As an application, we study the case of $W$ given by the quantized Weil algebra $qWg = Ug otimes Clg$ for $Lieg$ a reductive Lie algebra. The resulting cohomology of the canonical Weil differential gives a Clifford algebra, but the bilinear form vanishes on the space of primitive invariants of the semi-simple part. As an application, we consider the deformed Weil differential (following Freed, Hopkins and Teleman).
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ROHR, Rudolf Philippe. Transgression and Clifford algebras. In: Annales de l'Institut Fourier, 2009, vol. 59, n° 4, p. 1337-1358. https://archive-ouverte.unige.ch/unige:8522

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Deposited on : 2010-07-02

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