Characterization and enumeration of reflectable bases of types E6,7,8

Azam, Saeid; Soltani, Mohammad Bagher; Tomie, Masaya; Yoshii, Yōji

doi:10.1080/00927872.2021.2018448

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2023

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“…In Section 4, the characterization theorem of reflectable bases for reduced extended affine root systems is recorded from [AYY, Section 3] and [ASTY1]. Then the cardinality of elements of M c , M r and M m are investigated.…”

Section: Introductionmentioning

confidence: 99%

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

Azam¹,

Tan²

2023

Preprint

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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 posses the so called "the presentation by conjugation". In this work we give a characterization of 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 a Serre's type generators and relations.2010 Mathematics Subject Classification. 17B67 20F55 17B22 17B65. Key words and phrases. Extended affine root systems, extended affine Weyl groups, reflectable bases, elliptic Lie algebras, presentations of Lie algebras.

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Section: Introductionmentioning

confidence: 99%