# Computation of lattice isomorphisms and the integral matrix similarity problem

Seminar
Speaker
Henri Johnston (University of Exeter)
Date
15/06/2022 - 11:30 - 10:30Add to Calendar 2022-06-15 10:30:00 2022-06-15 11:30:00 Computation of lattice isomorphisms and the integral matrix similarity problem 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 ================================================ https://us02web.zoom.us/j/87856132062 Meeting ID: 878 5613 2062 Zoom -- see link below אוניברסיטת בר-אילן - Department of Mathematics mathoffice@math.biu.ac.il Asia/Jerusalem public
Place
Zoom -- see link below
Abstract

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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https://us02web.zoom.us/j/87856132062

Meeting ID: 878 5613 2062

Last Updated Date : 07/06/2022