ON BOHR SETS OF INTEGER-VALUED TRACELESS MATRICES.

In this paper we show that any Bohr-zero non-periodic set B of traceless integer-valued matrices, denoted by Λ, intersects non-trivially the conjugacy class of any matrix from Λ. As a corollary, we obtain that the family of characteristic polynomials of B contains all characteristic polynomials of matrices from Λ. The main ingredient used in this paper is an equidistribution result for an SLd(ℤ) random walk on a finite-dimensional torus deduced from Bourgain-Furman-Lindenstrauss-Mozes work [J. Amer. Math. Soc. 24 (2011), 231-280]. [ABSTRACT FROM AUTHOR]