Title
Clifford algebras, Möbius transformations, Vahlen matrices, and B-loops
Document Type
Article
Publication Date
1-1-2010
Abstract
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 ℝn. One notable achievement is a compact, convenient formula for the Möbius loop operation a * b = (a + b)(1 - ab)-1, where the operations on the right are those arising from the Clifford algebra (a formula comparable to (w+z)(1+wz)-1 for the Möbius loop multiplication in the unit complex disk).
Publication Source (Journal or Book title)
Commentationes Mathematicae Universitatis Carolinae
First Page
319
Last Page
331
Recommended Citation
Lawson, J. (2010). Clifford algebras, Möbius transformations, Vahlen matrices, and B-loops. Commentationes Mathematicae Universitatis Carolinae, 51 (2), 319-331. Retrieved from https://repository.lsu.edu/mathematics_pubs/598