Special first order systems in Clifford analysis and resolutions.
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)].
scientific article; zbMATH DE number 1779535
scientific article