Pseudo unitary conformal groups and Clifford algebras for standard pseudo hermitian spaces |
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Authors: | Email author" target="_blank">Pierre?AnglèsEmail author |
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Institution: | (1) U.F.R. M.I.G., Université Paul Sabatier, 118, Route de Narbonne, 31062 Toulouse Cedex 4, France |
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Abstract: | This paper, self-contained, deals with pseudo-unitary spin geometry. First, we present pseudo-unitary conformal structures
over a 2n-dimensional complex manifold V and the corresponding projective quadrics
for standard pseudo-hermitian spaces Hp,q. Then we develop a geometrical presentation of a compactification for pseudo-hermitian standard spaces in order to construct
the pseudo-unitary conformal group of Hp,q. We study the topology of the projective quadrics
and the “generators” of such projective quadrics. Then we define the space S of spinors canonically associated with the pseudo-hermitian scalar product of signature (2n−1, 2n−1). The spinorial group Spin U(p,q) is imbedded into SU(2n−1, 2n−1). At last, we study the natural imbeddings of the projective quadrics
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Keywords: | 15A66 17B37 20C30 |
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