Dual quaternions and slice functions: theory and applications

Abstract: The talk will present some recent results in the theory of slice functions over alternative *-algebras, introduced by Ghiloni and Perotti in 2011 as a generalization of the theory of quaternionic slice regular functions launched by Gentili and Struppa in 2006. The talk will focus on the algebra of dual quaternions. For this algebra, an explicit classification of zero divisors is available. This makes it possible to study the zero sets of slice functions, slice regular functions and polynomials over this algebra in full detail. This study can be applied to the open problem of factorizing motion polynomials over dual quaternions. The polynomials in this class, introduced by Hegedüs, Schicho, and Schröcker in 2013, correspond to rational rigid body motions in the Euclidean 3-space. Their factorizations correspond to linkages producing the same motions, so their classification is relevant to mechanism science. The main results presented have been proven jointly with Graziano Gentili and Tomaso Trinci.

Mathematics

Audience: researchers in the topic

Geometry Seminar - University of Florence

Series comments: If you are interested in attending, please send a message to daniele.angella@unifi.it or francesco.pediconi@unifi.it.