Quaternion arithmetic: factorization and geometry
 
 
Description:  The ring of the so called Hurwitz integers, which contains the integral quaternions, being both a left and a right PID, is the appropriate ring inside the quaternions in which to study arithmetical questions. The fact that it is a non commutative ring entails some complications, but also some surprises, as well as some interesting open problems. In this talk we will describe Conway and Smith metacommutation problem, and some almost forgotten results on the related ring of Lipschitz integers. We will then present some results, obtained in joint work with Luis Roçadas, on some relationships between the arithmetic and the geometry of Lipschitz integers, namely certain divisibility relations between a given Lipschitz integer and some other integers built from it using the vector product. Some speculations on a possible integer factorization method involving quaternion arithmetic will also be presented. No previous knowledge pertaining to these matters will be assumed.
Date:  2013-04-17
Start Time:   14:00
Speaker:  António Machiavelo (CMUP/Univ. Porto)
Institution:  CMUP/Universidade do Porto
Place:  Room 5.5 (DMUC)
Research Groups: -Algebra and Combinatorics
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