Scientific article
Open access

Pure Spinors on Lie groups

Published inAstérisque, no. 327, p. 131-199
Publication date2010

For any manifold M, the direct sum TM oplus T*M carries a natural inner product given by the pairing of vectors and covectors. Differential forms on M may be viewed as spinors for the corresponding Clifford bundle, and in particular there is a notion of emph{pure spinor}. In this paper, we study pure spinors and Dirac structures in the case when M=G is a Lie group with a bi-invariant pseudo-Riemannian metric, e.g. G semi-simple. The applications of our theory include the construction of distinguished volume forms on conjugacy classes in G, and a new approach to the theory of quasi-Hamiltonian G-spaces.

  • arxiv : math.DG
Citation (ISO format)
ALEKSEEV, Anton, BURSZTYN, Henrique, MEINRENKEN, Eckhard. Pure Spinors on Lie groups. In: Astérisque, 2010, n° 327, p. 131–199.
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Article (Accepted version)
ISSN of the journal0303-1179

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