يك مشخصه‌سازي از سيستم‌هاي ريشه آفين توسيعي مينيمال (كمين)

In the theory of extended affine Lie algebras, finding suitable presentations for extended affine Weyl groups is of particular interest. It has been shown that only elements of a certain subclass of extended affine Weyl groups, whose root systems are minimal extended affine root systems, admit a "presentation by conjugation". In the general case, a weaker representation, called the generalized presentation by conjugation, is provided for extended affine Weyl groups. When the extended affine root system is minimal, the "generalized presentation by conjugation" coincides with the presentation by conjugation. This motivates the main goal of this thesis, which is to present a characterization of reduced minimal extended affine root systems. This characterization is described in terms of reflectable bases, which are analogous to the concept of bases for finite an‎d affine root systems. An extended affine root system of nullity 2 is known as an "elliptic root system", an‎d elements of a certain class of Lie algebras whose root systems are elliptic are called "elliptic Lie algebras". Another aim of this thesis is to investigate the concept of reflectable bases for the construction of elliptic Lie algebras of rank 1 via generators an‎d Serre-type relations.

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