Resolution of the k-Dirac operator

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F18%3A10386086" target="_blank" >RIV/00216208:11320/18:10386086 - isvavai.cz</a>
Result on the web
<a href="https://arxiv.org/pdf/1705.10168.pdf" target="_blank" >https://arxiv.org/pdf/1705.10168.pdf</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s00006-018-0830-6" target="_blank" >10.1007/s00006-018-0830-6</a>

Result language
angličtina
Original language name
Resolution of the k-Dirac operator
Original language description
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.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10101 - Pure mathematics

Project
<a href="/en/project/GA17-01171S" target="_blank" >GA17-01171S: Invariant differential operators and their applications in geometric modelling and control theory</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2018
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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