Resolution of the k-Dirac operator

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

Resolution of the k-Dirac operator

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

Resolution of the k-Dirac operator

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/GA17-01171S" target="_blank" >GA17-01171S: Invariantní diferenciální operátory a jejich aplikace v geometrickém modelování a v teorii optimálního řízení</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2018

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Advances in Applied Clifford Algebras

ISSN

0188-7009

e-ISSN

—

Svazek periodika

2018[28]

Číslo periodika v rámci svazku

1

Stát vydavatele periodika

CH - Švýcarská konfederace

Počet stran výsledku

19

Strana od-do

—

Kód UT WoS článku

000427260400014

EID výsledku v databázi Scopus

2-s2.0-85041589388