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arXiv · 2303.15884

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

Saeid Azam·Fatemeh Parishani·Shaobin Tan
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Abstract

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.

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Saeid Azam, Fatemeh Parishani, Shaobin Tan. 2023-03-28. A characterization of minimal extended affine root systems (Relations to Elliptic Lie Algebras). https://arxiv.org/abs/2303.15884

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