Quaternions, Dual Quaternions and Clifford algebras

J.M. Selig, London South Bank University.
Date: 24th January, 2023, Time: 14:00.
Place: Dokuz Eylül Üniv., Tınaztepe Yerleşkesi, Fen Fak. Matematik Böl.

Abstract:After a brief review of Hamilton’s quaternions and how they can be used to represent rotations, Clifford’s dual quaternions will be discussed. The use of this algebra to represent rigid-body displacements will be explained. As will the relation to the Study quadric. The representation of twists, infinitesimal rigid-body displacements, will also be considered. Finally, the notion of Clifford algebras will be introduced and various examples will be considered. In particular, examples rep-resenting the algebra of 3-dimensional Euclidean geometry will be outlined.