On the presentations of extended affine Weyl groups.

DOI10.2977/PRIMS/1207921079zbMath1144.20020OpenAlexW2081771232MaRDI QIDQ928394

Saeid Azam, Valiollah Shahsanaei

Publication date: 18 June 2008

Published in: Publications of the Research Institute for Mathematical Sciences, Kyoto University (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2977/prims/1207921079

zbMATH Keywords

generators and relationsextended affine root systemspresentations by conjugationsimply laced extended affine Weyl groups

Mathematics Subject Classification ID

Generators, relations, and presentations of groups (20F05) Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras (17B67) Reflection and Coxeter groups (group-theoretic aspects) (20F55) Simple, semisimple, reductive (super)algebras (17B20)

Related Items (8)

The Structure of a Presented Group Associated to an Extended Affine Root System ⋮ Reflectable bases for affine reflection systems ⋮ Combinatorics of extended affine root systems (type A1) ⋮ A graph-theoretical classification for reflectable bases ⋮ Extended Affine Weyl Groups: Presentation by Conjugation via Integral Collection ⋮ Extended affine Weyl groups of type \(A_1\). ⋮ Presentation by conjugation for \(A_1\)-type extended affine Weyl groups. ⋮ Presentation by conjugation for \(A_1\)-type extended affine Weyl groups.

Cites Work

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• Extended affine root systems. I: Coxeter transformations
• Extended affine Weyl groups
• Defining relations of Weyl groups for extended affine root systems \(A_ l^{(1,1)}\), \(B_ l^{(1,1)}\), \(C_ l^{(1,1)}\), \(D_ l^{(1,1)}\)
• Extended affine root systems. III: Elliptic Weyl groups
• Nonreduced extended affine Weyl groups.
• Simply laced extended affine Weyl groups (a finite presentation).
• Extended affine Lie algebras and their root systems
• A presentation for reduced extended affine weyl groups

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