### Computation of lattice isomorphisms and the integral matrix similarity problem

Heilbronn Number Theory Seminar

27th April 2022, 4:00 pm – 5:00 pm

Fry Building, 2.04

Let A be a finite-dimensional algebra over a number field and let Lambda be an order in A. Under certain hypothesis on A, we give an efficient algorithm that given two Lambda-lattices X and Y, determines whether X and Y are isomorphic, and if so, computes an explicit isomorphism X -> Y. As an application, we give an algorithm for the following long-standing problem: given a positive integer n and two n x n integral matrices A and B, determine whether A and B are similar over Z, and if so, return a matrix C in GL_n(Z) such that B= CAC^-1. This is joint work with Werner Bley and Tommy Hofmann. The preprint is available here: https://arxiv.org/abs/2202.03526

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