There are many well known interactions between geometry and algebra. In particular, finite geometry has many applications to Clifford Algebras. One example is in finding sets of operators to label spinor states, and this leads to the question of understanding the structure of certain subspaces of the power set P(S). [Here, given a vector space V , we let S denote the set of points in the corresponding projective space.] In this talk, we discuss some of these applications, and in particular investigate the use of geometrical structures to classify algebraic forms. Our main concern is with finite projective geometries, and the classification is related to actions under the general linear group.

This research makes use of symbolic algebra packages to search for the list of canonical forms, and in implementing isomorphisms between the two areas. We discuss some of the issues in using symbolic algebra systems to investigate geometrical structures, especially ways of identifying geometric objects on different orbits under group actions. Of particular interest are the actions of projective general linear groups on the geometric sets. We briefly mention some of the applications of these results.

n.a.gordon@dcs.hull.ac.uk

Department of Computer Science,
University of Hull, HU6 7RX, U.K.