Measurably Nonconjugate Higher-Rank Abelian Non-Cartan Actions
by
Bakker, Lennard
Department of Mathematics, Brigham Young University

We apply algebraic techniques to the construction of non-Cartan hyperbolic irreducible

higher-rank abelian actions by linear toral automorphisms that are not algebraically

conjugate and hence, by rigidity, are not measurably conjugate. The algebraic techniques

employed come from the theory of real algebraic number fields and from the theory of

generalized symmetries and their multipliers for quasiperiodic flows. We illustrate the

construction for rank 2 actions in dimensions 4 and 5.

Date received: March 27, 2007