Root Systems and Dynkin Diagrams
نویسنده
چکیده
In 1969, Murray Gell-Mann won the nobel prize in physics “for his contributions and discoveries concerning the classification of elementary particles and their interactions.” He is the scientist who first used the word quark, and he was the first to describe the SU3(C) flavor symmetry of the hadrons. By organizing the particles according to the root system of the lie algebra su3(C) associated to the group of symmetries, he predicted the existence of new particles, which were later found experimentally. So root systems provide a key element in mathematical models for quantum systems, which is one reason that we might want to understand them. Root systems are also the key ingredient in the classification of finite-dimensional, simple Lie algebras. The symmetries of root systems are the Weyl groups, one of the types of Coxeter groups, which are of interest in geometry group theory.
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