A Lecture about classification of Lorentzian Kac-Moody algebras of the rank three

Abstract

This is the announcement and partly the review of our results about classification of Lorentzian Kac-Moody algebras of the rank three. One of our results gives the classification of Lorentzian Kac-Moody algebras with denominator identity functions which are holomorphic reflective automorphic forms with respect to paramodular groups. Almost all of them were found in our paper ``Automorphic forms and Lorentzian Kac-Moody algebras. Parts I, II'', Intern. J. Math. 9 (1998), 153-275. Our main result gives classification of all reflective meromorphic automorphic products with respect to paramodular groups. This is mainly a presentation of our lectures given during the Workshop: ``Applications to Quantum Field Theory'', October 23 - 27, 2000, in the Newton Mathematical Institute at Cambridge.