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Vahlen Matrices for Non-Definite Metrics

In: Clifford Algebras with Numeric and Symbolic Computations

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  • J. Cnops

    (Universiteit Gent)

Abstract

The relation between Möbius transformations -conformal mappings mapping generalized spheres to spheres- of a Euclidean or pseudo-Euclidean space, two by two matrices with entries in a Clifford algebra, and covering groups like O(p + 1, q + 1) are well known. Vahlen gave, already in the beginning of this century, a characterization of matrices describing Möbius transformations for the Euclidean case (without using the background of orthogonal groups). In this paper we give a criterion, in a form quite close to Vahlen’s, for the general case.

Suggested Citation

  • J. Cnops, 1996. "Vahlen Matrices for Non-Definite Metrics," Springer Books, in: Rafał Abłamowicz & Josep M. Parra & Pertti Lounesto (ed.), Clifford Algebras with Numeric and Symbolic Computations, pages 155-164, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4615-8157-4_10
    DOI: 10.1007/978-1-4615-8157-4_10
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