Automorphism groups of geometric lattices
by
Rüdiger Göbel
University Essen
Coauthors: Manfred Dugas (Baylor University)

At a conference on abelian groups and ordered structures in 1999 at Tulane Graetzer asked a question about realizing groups as automorphism groups of modular lattices with additional 'geometric properties'. In a joint paper with Dugas we represent any group as the automorphism group of such a lattice. Note that there is a long list of relatives of this theorem for various (other) lattices with proofs based on lattice theory using gluing-pasting techniques; see also Brehm's work and Graetzer's (recent edition of his) book on lattices. We will proceed differently:

The nice features of our proof are:

1. Using powerful methods applied for realizing algebras as endomorphism algebras of particular modules.
2. Extending the fundamental theorem for projective geometry in such a way that it can be used for modules constructed in (1).

Date received: June 14, 2000

Copyright © 2000 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caee-97.