A characterization of minimal extended affine root systems (Relations to Elliptic Lie Algebras)

Extended affine root systems appear as the root systems of extended affine Lie algebras. A subclass of extended affine root systems, whose elements are called ``minimal" turns out to be of special interest mostly because of the geometric properties of their Weyl groups; they possess the so-called ``presentation by conjugation". In this work, we characterize minimal extended affine root systems in terms of ``minimal reflectable bases" which resembles the concept of the ``base" for finite and affine root systems. As an application, we construct elliptic Lie algebras by means of Serre's type generators and relations.