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Advances in Applied Clifford Algebras

, Volume 27, Issue 1, pp 33–44 | Cite as

Conformal Groups and Vahlen Matrices

  • Jacques Helmstetter
Article

Abstract

This article recalls some facts about the conformal group \({{\rm Conf}(V, Q)}\) of a quadratic space (V, Q); in particular, there is a surjective group morphism \({{\rm O}(V^{\dag}, Q^{\dag}) \rightarrow {\rm Conf}(V, Q)}\), where \({(V^{\dag}, Q^{\dag})}\) is the orthogonal sum of (V, Q) and a hyperbolic plane; its kernel is a group of order two. Then it explains how the elements of \({{\rm O}(V^{\dag}, Q^{\dag})}\) and \({{\rm Conf}(V, Q)}\) can be represented by Vahlen matrices. And finally, it recalls some properties of Vahlen matrices.

Keywords

Conformal transformations Vahlen matrices 

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Copyright information

© Springer Basel 2015

Authors and Affiliations

  1. 1.Institut FourierUniversité de Grenoble ISaint-Martin d’HèresFrance

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