Abstract
The Cliffordian formalism through the pure spinor theory of Chevalley-Cartan enables one to construct explicitely a torogonal lifting of some reduction of a pseudo-Riemannian structure. Some applications of this construction are given, for instance, in relation with the geometric quantization in Mathematical Physics.
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References
— Cartan, E. (1938) Leçons sur la théorie des spineurs. Hermann, Paris.
— Chevalley, C. (1954). The algebraic theory of spinors. Columbia University press. New-York.
— Crumeyrolle, A. (1975). Periodica. Math. Hungarica 6(2).
— Frenkel, J. (1955). Cohomologie à valeurs dans un faisceau non abélien. C.R. Acad. Sci. Paris, 240.
— Greub, W., Petry, H.R. (1978). On the lifting of structure groups II, Proc. Bonn 1977. Springer Lect. Notes in Math. 676.
— Karrer, G. (1973). Darstellung von Clifford Bündeln. Ann. Acad. Sci. Fennicae, serie A, 1, 521.
— Kostant, B. (1970). Quantization and unitary representations. Lect. notes in Math. vol 170. Springer. New-York.
— Souriau, J.M. (1966). Commun. Math. Phys. 1.
— Timbeau, J. a) (1987) Le rôle du concept torogonal dans une préquantification géométrique sur les variétés pseudo-riemanniennes. C.R. Acad. Sci. Paris, t. 305. Série I. b) (1986) Structure torogonale et quantification sur des variétés pseudo-riemanniennes — Thèse — Toulouse c) Twisting procedure on torogonal structures-to appear.
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© 1992 Springer Science+Business Media Dordrecht
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Timbeau, J. (1992). Clifford algebras and torogonal structures. In: Micali, A., Boudet, R., Helmstetter, J. (eds) Clifford Algebras and their Applications in Mathematical Physics. Fundamental Theories of Physics, vol 47. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-8090-8_16
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DOI: https://doi.org/10.1007/978-94-015-8090-8_16
Publisher Name: Springer, Dordrecht
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