TGTS Tetrahedral Geometry/Topology Seminar

    Date: Friday 5 March 2010, 4:30pm
Location: Hempfield High School, Room 213
 Speaker: Craig Culbert, Franklin and Marshall College
   Title: Cayley-Dickson algebras, vector products, and finite geometry

Abstract. Algebras derived from the Cayley-Dickson process over
the real numbers include the quaternion division algebra and the
octonion alternative division algebra. Both these algebras have been
used to examine their associated real spaces using products derived from
the commutator and associator of the algebras. Similar ideas are
examined for the sedenion algebra and other algebras derived from the
Cayley-Dickson process. This surprisingly involves a finite geometry
that is related to the subalgebras of the Cayley-Dickson algebra. This
finite geometry can be used to make representations of vector products
defined using the commutator and associator.