Tuesday, January 26, 14:00
Carsten Dietzel, Modular noetherian right l-groups
Right l-groups are groups that are equipped with a lattice structure that is
invariant under right-multiplication. Those with a strong order unit and
distributive, noetherian lattice structure have been characterized by Chouraqui
and Rump - these are exactly the structure groups of non-degenerate, involutive
set-theoretic solutions to the Yang-Baxter equation.
What can be said about the more general class of modular noetherian right
l-groups with strong order unit? Rump proved that each such group has a
distinguished strong order interval that is a modular geometric lattice. By this
result, we know part of the local lattice structure in this class of groups.
After giving an overview of these results, emphasis will be put on the class of
desarguesian right l-groups, that is, modular noetherian right l-groups with a
desarguesian strong order interval. I will present two classes of desarguesian
right l-groups that can be obtained from matrix rings and skew polynomial rings,
respectively. It turns out that these constructions are, in fact, instances of a
representation theorem for desarguesian right l-groups of dimension 4 or greater.