Pure PGR Seminar - Cayley-Dickson construction, Simon Rea (Southampton) Seminar

Event details

The real and complex numbers, which are the bread and butter of every student of mathematics, can be endowed with several types of algebraic structures. As normed division algebras, they have only two companions: the quaternions and the octonions. The former were famously discovered by Hamilton in 1843, while the latter suffered an inglorious birth at the hands of Hamilton's college friend John Graves later that same year. In this talk we will discuss the Cayley-Dickson construction which shows how R, C, H and O fit nicely at the start of an infinite sequence of algebras, doubling in dimension at each step. This will help us understand why multiplication is not commutative in H and not associative in O.