The Mutation Game, Coxeter-Dynkin Graphs, and Generalized Root Systems

• 来源期刊: 代数集刊（英文版）
• 关键词: directed graph Dynkin diagram Coxeter group mutation game root system
• 年，卷（期）: 2020,（1）
• 页码范围: 55-78
• 页数: 24页
• 语种: 英文
• DOI: 10.1142/S1005386720000061

摘要

We introduce the mutation game on a directed multigraph,which is dual to Mozes' numbers game.This new game allows us to create geometric and combinatorial structure that allows generalization of root systems to more general graphs.We interpret Coxeter-Dynkin diagrams in this multigraph context and exhibit new geometric forms for the associated root systems.