Reachability problems in quaternion matrix and rotation semigroups

Bell

doi:10.1016/j.ic.2008.06.004

Reachability problems in quaternion matrix and rotation semigroups

Bell

Authors

Paul Bell p.c.bell@keele.ac.uk

Abstract

We examine computational problems on quaternion matrix and rotation semigroups. It is shown that in the ultimate case of quaternion matrices, in which multiplication is still associative, most of the decision problems for matrix semigroups are undecidable in dimension two. The geometric interpretation of matrix problems over quaternions is presented in terms of rotation problems for the 2- and 3-sphere. In particular, we show that the reachability of the rotation problem is undecidable on the 3-sphere and other rotation problems can be formulated as matrix problems over complex and hypercomplex numbers.

Acceptance Date	Jun 10, 2008
Publication Date	Nov 1, 2008
Journal	Information and Computation
Print ISSN	0890-5401
Publisher	Elsevier
Pages	1353 - 1361
DOI	https://doi.org/10.1016/j.ic.2008.06.004
Publisher URL	https://www.sciencedirect.com/science/article/pii/S0890540108000771?via%3Dihub