Abstract
Möbius transformations in any dimension can be expressed through 2x2 matrices with Clifford numbers as entries. This technique is relatively unknown in spite of having been introduced as early as 1902. The present paper should be viewed as a strong endorsement for the use of Clifford algebras in this particular context. In addition to an expository introduction to Clifford numbers it features a discussion of the fixed points and classification of Möbius transformations.
Research supported by National Science Foundation and ForschungsInstitut für Mathematik
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References
L. Ahlfors: ‘Möbius transformations and Clifford numbers’, Differential Geometry and Complex Analysis — in memory of H.E. Rauch, Springer Verlag 1985.
L. Ahlfors: ‘On the fixed points of Möbius transformations in Rn’, Ann. Acad. Sci. Fenn. Ser. AI, Vol. 10, 1984.
R. Fueter: ‘Sur les groupes improprement discontinus’, C. R. Acad. Sci. Paris 182, 432–434, 19
H. Maass: ‘Automorphe Funktionen von mehreren Veränderlichen und Dirichletsche Reihen’, Abh. Math. Sem. Univ. Hamburg 16, 53–104, 1949.
K.Th. Vahlen: ‘Über Bewegungen und complexe Zahlen’, Math. Annalen 55, 585–593, 1902.
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© 1986 D. Reidel Publishing Company
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Ahlfors, L.V. (1986). Clifford Numbers and Möbius Transformations in Rn . In: Chisholm, J.S.R., Common, A.K. (eds) Clifford Algebras and Their Applications in Mathematical Physics. NATO ASI Series, vol 183. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-4728-3_15
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DOI: https://doi.org/10.1007/978-94-009-4728-3_15
Publisher Name: Springer, Dordrecht
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