Some arithmetic groups that are not left orderable

  • Date: 03/19/2007

Dave Morris (University of Lethbridge)


University of British Columbia


It is known that finite-index subgroups of the arithmetic group SL(3,Z)
are not left orderable. (In other words, they have no interesting
actions on the real line.) This naturally led to the conjecture that
most other arithmetic groups (of higher real rank) also are not left
orderable. The problem remains open, but joint work with Lucy Lifschitz
verifies the conjecture for many examples, including every finite-index
subgroup of SL(2,Z[sqrt(3)]) or SL(2,Z[1/3]). The proofs are based on
the fact, proved by D.Carter, G.Keller, and E.Paige, that every element
of these groups is a product of a bounded number of elementary

Other Information: 

Algebraic Geometry Seminar 2007