UTA Department of Mathematics

Algebra Seminar

Date/Time/Room: Friday (10/29/2004) at 4:00pm in 487 Pickard Hall

Speaker: Bill Purpura, Department of Mathematics, University of Texas at Arlington

"Spreads, Matrix Spread Sets, and Lifting"

Abstract: A translation plane is a projective plane whose translation group acts regularly on its affine points. Translation planes may be represented by matrix spread sets over V(n,q)=GF(q)^n, which are special subsets of GL(n,q) along with O. Equivalently, translation planes may be represented as spreads of V(2n,q), which are special partitions of V(2n,q). In this talk, we explore these representations of translation planes. If time permits, we will discuss a method developed by the Japanese mathematicians Hiramine, Matsumoto, and Oyama, by which matrix spread sets over V(2,q) "lift" to matrix spread sets over V(4,q).