The octonion integers
- Prelegent(ci)
- Derek A. Smith
- Afiliacja
- Lafayette College, USA
- Termin
- 10 stycznia 2008 12:00
- Pokój
- p. 5820
- Seminarium
- Seminarium „Algebra”
Abstract.
The real numbers, the complex numbers, the quaternions,
and the octonions comprise the four composition algebras.
The first three are usually seen to be the well-behaved
members of the family; the octonions, to quote John Baez,
are "the crazy old uncle nobody lets out of the attic."
I would like to let the octonions out of the attic to
introduce some of its fundamental properties, with an eye toward its
most important ring of integers, the integral Cayley numbers of
Coxeter. A beautiful and remarkably simple algorithm of Rehm leads
to a unique factorization theorem for this ring, despite its
non-associativity. Just as remarkably, there are several
elementary questions about factorization in this and related
rings that remain unanswered.