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Mathematics and Statistics Colloquium
Date/Time/Room:
Friday (10/13/2006) at 2:30pm in 304 Pickard Hall "Division Algebras"Abstract: On a bridge in Dublin in 1843, Hamilton is supposed to have carved ``i^2 = j^2 = k^2 = ijk = -1$'' which defines, over the reals, the so called algebra of quaternions, H. This algebra H is a sort of ``noncommutative'' field, where every nonzero element has an inverse but, in general, xy does not equal yx. Furthermore, as a vector space, H is finite dimensional (in fact 4 dimensional). By definition, this makes H a _division algebra_. The problem behind this talk is the question of finding or describing all division algebras. We will discuss what this means, and survey some of the results in this area. A theme we will emphasize is that the problem is concrete, but the tools one can use to study it are remarkably diverse.
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