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Title: From hermitean clifford analysis to subelliptic dirac operators on odd dimensional spheres and other CR manifolds
Author: Cerejeiras, P.
Kahler, U.
Ryan, J.
Keywords: Kohn Laplacian
Kohn Dirac operator
CR manifolds
Issue Date: Oct-2018
Publisher: Springer International Publishing
Abstract: We show that the two Dirac operators arising in Hermitian Clifford analysis are identical to standard differential operators arising in several complex variables. We also show that the maximal subgroup that preserves these operators are generated by translations, dilations and actions of the unitary n-group. So the operators are not invariant under Kelvin inversion. We also show that the Dirac operators constructed via two by two matrices in Hermitian Clifford analysis correspond to standard Dirac operators in euclidean space. In order to develop Hermitian Clifford analysis in a different direction we introduce a sub elliptic Dirac operator acting on sections of a bundle over odd dimensional spheres. The particular case of the three sphere is examined in detail. We conclude by indicating how this construction could extend to other CR manifolds.
Peer review: yes
ISBN: 978-3-030-00047-9
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Appears in Collections:CHAG - Capítulo de livro

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