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A Construction of a Skewaffine Structure in Laguerre Geometry

Andrzej Matraś (2006)

Bulletin of the Polish Academy of Sciences. Mathematics

J. Andre constructed a skewaffine structure as a group space of a normally transitive group. In this paper his construction is used to describe the structure of the set of circles not passing through a point of a Laguerre plane. Sufficient conditions to ensure that this structure is a skewaffine plane are given.

Bemerkungen zur n -dimensionalen reellen Möbiusgeometrie.

Hermann Schaal (1991)

Applications of Mathematics

Dieser Artikel befasst sich mit den Gründen der reellen n -dimensionalen Möbiusgeometrie. Hier werden 2 Behauptungen bewiessen: 1) Die Möbiustransformationen sind die einzigen M -spärentreuen Bijektionen von M n : = n { } ; 2) Jede Möbiumstransformation ist Produkt von maximal n + 2 Spiegelungen, wobei neben Spiegelungen an Hyperebenen höchsterns zwei Spiegelungen an Hypersphären benötigt werden.

Clifford algebras, Möbius transformations, Vahlen matrices, and B -loops

Jimmie Lawson (2010)

Commentationes Mathematicae Universitatis Carolinae

In this paper we show that well-known relationships connecting the Clifford algebra on negative euclidean space, Vahlen matrices, and Möbius transformations extend to connections with the Möbius loop or gyrogroup on the open unit ball B in n -dimensional euclidean space n . One notable achievement is a compact, convenient formula for the Möbius loop operation a * b = ( a + b ) ( 1 - a b ) - 1 , where the operations on the right are those arising from the Clifford algebra (a formula comparable to ( w + z ) ( 1 + w ¯ z ) - 1 for the Möbius loop multiplication...

Conos de luz.

Javier Lafuente López (1992)

Revista Matemática de la Universidad Complutense de Madrid

Using a new characterization of the Lorentz quadrics, we establish a reformulation of the Special Relativity Theory.

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