A Lie algebra approach to difference sets
Presented by:Gyula Karolyi, UQ
Date:Tue 7 Aug, 3:00 pm
Venue:Room 442, Building 67
Let A and B be subsets of a torsion free abelian group G. Because G admits a linear ordering, it is easy to see that the sumset A + B has at least |A| + |B| - 1 different elements. According to the Cauchy-Davenport theorem, the statement remains valid in the group of integers modulo any prime p > |A| + |B| - 2. In this talk we demonstrate how the simple notion of the adjoint representation leads to the proof in the special case when B = - A. A minute modification then gives a purely matrix algebraic proof of the Cauchy-Davenport theorem.
Only basic knowledge of linear algebra is needed to follow the talk.