Resolution of the $k$-Dirac operator
Abstract
This is the second part in a series of two papers. The -Dirac complex is a complex of differential operators which are natural to a particular -graded parabolic geometry. In this paper we will consider the -Dirac complex over a homogeneous space of the parabolic geometry and as a first result, we will prove that the -Dirac complex is exact with formal power series at any fixed point. Then we will show that the -Dirac complex descends from an affine subset of the homogeneous space to a complex of linear, constant coefficient differential operators and that the first operator in the descended complex is the -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 -Dirac operator.
Keywords
Cite
@article{arxiv.1705.10168,
title = {Resolution of the $k$-Dirac operator},
author = {Tomas Salac},
journal= {arXiv preprint arXiv:1705.10168},
year = {2018}
}