In 1985, K. Saito introduced elliptic root systems as root systems belonging to a real vector space F equipped with a symmetric bilinear form I with signature (l, 2, 0). Such root systems are studied in view of simply elliptic singularities which are surface singularities with a regular elliptic curve in its resolution. K. Saito had classified elliptic root systems R with its one-dimensional subspace G of the radical of I, in the case when R/G ⊂ F/G is a reduced affine root system. In our joint work with A. Fialowski and Y. Saito, we have completed its classification; we classified the pair (R,G) whose quotient R/G ⊂ F/G is a non-reduced affine root system. In this talk, we give an overview of elliptic root systems and describe some of the new root systems we have found.
This video is part of the European Non-Associative Algebra Seminar series.
