Hurwitz problem, harmonic morphisms and generalized Hadamard matrices
type: Item
instance of: scholarly article
title: Hurwitz problem, harmonic morphisms and generalized Hadamard matrices
zbMATH Open document ID: 0820.15020
DOI: 10.1016/0377-0427(94)90250-X
author: Dominique Lambert
author: A. Ronveaux
published in: Journal of Computational and Applied Mathematics
publication date: 1995-09-21T00:00:00Z
review text: The authors use real representations of real Clifford algebras associated with the Hurwitz problem of factorization of algebraic sums of squares in order to construct harmonic morphisms defined on Euclidean spaces or on pseudo-Euclidean spaces endowed with a metric of neutral signature. In general the composition of two harmonic maps is not a harmonic map. But the composition of a harmonic morphism with a harmonic map is also harmonic. The result of the paper is an extension of the construction given by \textit{P. Baird} [Harmonic maps with symmetric, harmonic morphisms and deformations of metrics (1983; Zbl 0515.58010)] in the framework of the theory of harmonic maps defined on Euclidean spaces. The construction of harmonic morphisms considered in the paper can be used to generate generalized Hadamard matrices which are used in design theory. Moreover, on the base of the Hurwitz transformations generalizing the Kustaanheimo-Steifel transformations the authors give a way to construct a class of harmonic functions on \(\mathbb{R}^{m+1}\) from those of \(\mathbb{R}^{s+ 1}\) and conversely.
Mathematics Subject Classification ID: 15A66
Mathematics Subject Classification ID: 58E20
Mathematics Subject Classification ID: 05B20
zbMATH DE Number: 739558
zbMATH Keywords: real representations
zbMATH Keywords: real Clifford algebras
zbMATH Keywords: Hurwitz problem
zbMATH Keywords: factorization
zbMATH Keywords: algebraic sums of squares
zbMATH Keywords: harmonic morphisms
zbMATH Keywords: pseudo- Euclidean spaces
zbMATH Keywords: Hadamard matrices
zbMATH Keywords: Hurwitz transformations
zbMATH Keywords: Kustaanheimo-Steifel transformations
reviewed by: Nikolai I. Osetinski
MaRDI profile type: Publication
cites work: Q3662315
cites work: Q3737429
cites work: Another Report on Harmonic Maps
cites work: Cliffordalgebren und neue isoparametrische Hyperflächen
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cites work: An algebraic and geometric approach to non-bijective quadratic transformations
cites work: Pseudo-Euclidean Hurwitz pairs and the Kaluza-Klein theories
cites work: Pseudo-Euclidean Hurwitz pairs in any signature
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description: scientific article; zbMATH DE number 739558