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Resolution of the k-Dirac operator

Publikace na Matematicko-fyzikální fakulta |
2018

Tento text není v aktuálním jazyce dostupný. Zobrazuje se verze "en".Abstrakt

This is the second part in a series of two papers. The k-Dirac complex is a complex of differential operators which are naturally associated to a particular |2|-graded parabolic geometry.

In this paper we will consider the k-Dirac complex over the homogeneous space of the parabolic geometry and as a first result, we will prove that the k-Dirac complex is formally exact (in the sense of formal power series). Then we will show that the k-Dirac complex descends from an affine subset of the homogeneous space to a complex of linear and constant coefficient differential operators and that the first operator in the descended complex is the k-Dirac operator studied in Clifford analysis.

The main result of this paper is that the descended complex is locally exact and thus it forms a resolution of the k-Dirac operator.