Clifford Analysis, Clifford Algebras and Their Applications
Mathematics & Statistics
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 COQ(V), defined as the direct product of the orthogonal group OQ(V) with dilations. Utilizing the correspondence between conformal orthogonal group elements and ``decomposable'' elements of the associated Clifford algebra, ClQ(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.
G.S. Staples, D. Wylie. Clifford algebra decompositions of conformal orthogonal group elements, Clifford Analysis, Clifford Algebras and Their Applications, 4 (2015), 223-240