Clifford Algebra Decompositions of Conformal Orthogonal Group Elements

Authors

G. Stacey Staples, Southern Illinois University Edwardsville
David Wylie

Document Type

Article

Publication Date

2015

Publication Title

Clifford Analysis, Clifford Algebras and Their Applications

Department

Mathematics & Statistics

Abstract

Beginning with a finite-dimensional vector space V equipped with a nondegenerate quadratic form Q, we consider the decompositions of elements of the conformal orthogonal group CO_Q(V), defined as the direct product of the orthogonal group O_Q(V) with dilations. Utilizing the correspondence between conformal orthogonal group elements and ``decomposable'' elements of the associated Clifford algebra, Cl_Q(V), a decomposition algorithm is developed. Preliminary results on complexity reductions that can be realized passing from additive to multiplicative representations of invertible elements are also presented with examples. The approach here is based on group actions in the conformal orthogonal group. Algorithms are implemented in Mathematica using the CliffMath package.

Recommended Citation

G.S. Staples, D. Wylie. Clifford algebra decompositions of conformal orthogonal group elements, Clifford Analysis, Clifford Algebras and Their Applications, 4 (2015), 223-240