Special first order systems in Clifford analysis and resolutions.
type: Item
instance of: scholarly article
title: Special first order systems in Clifford analysis and resolutions.
zbMATH Open document ID: 1134.15302
DOI: 10.4171/ZAA/1064
published in: Zeitschrift für Analysis und ihre Anwendungen
publication date: 2002-10-14T00:00:00Z
review text: The authors generalize Clifford analysis in various ways using the notion of abstract vector variables. First order partial differential systems are used to describe several combinatorial systems and related geometries. A remarkable number of such systems is studied and explicite resolutions are given using the computer algebra program \texttt{CoCoA}. The paper comes up with some conjectures and a list of open research problems. The computer algebra is not able to deal with all examples in full detail. The relation to homology is not made explicit. It should be compared with the authors' work [in: Clifford analysis and its applications. Proceedings of the NATO advanced research workshop, Prague, Czech Republic, October 30-November 3, 2000. Dordrecht: Kluwer Academic Publishers. NATO Sci. Ser. II, Math. Phys. Chem. 25, 267--282 (2001; Zbl 1022.30049)].
Mathematics Subject Classification ID: 15A66
Mathematics Subject Classification ID: 30G35
Mathematics Subject Classification ID: 35A25
Mathematics Subject Classification ID: 35A27
zbMATH DE Number: 1779535
zbMATH Keywords: Abstract vector variables
zbMATH Keywords: monogenetic functions of higher spin
zbMATH Keywords: matrix variables
zbMATH Keywords: combinatorial systems
zbMATH Keywords: resolutions
zbMATH Keywords: syzygies
author: Irene Sabadini
author: Frank Sommen
reviewed by: Bertfried Fauser
describes a project that uses: CoCoA
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.4171/zaa/1064
OpenAlex ID: W2015519437
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description: scientific article; zbMATH DE number 1779535