Lattice isomorphism and the integral matrix similarity problem

Abstract: Deciding whether two lattices over orders of finite-dimensional algebras over number fields is a classical problem in algorithmic number theory. We present a new algorithm for this problem, assuming that the Wedderburn decomposition of the algebra behaves nice. As an application we discuss the connection to the similarity problem for integral matrices (the conjugacy problem in GL(n, Z)). The resulting algorithm for the latter problem is the first with proven complexity and performs very well in practice. This is joint work with Werner Bley and Henri Johnston.

algebraic geometrynumber theory

Audience: researchers in the topic

Leiden Algebra, Geometry, and Number Theory Seminar