By Jürgen Fuchs, Christoph Schweigert
This is often an creation to Lie algebras and their functions in physics. First illustrating how Lie algebras come up clearly from symmetries of actual platforms, the ebook then offers an in depth advent to Lie algebras and their representations, masking the Cartan-Weyl foundation, uncomplicated and affine Lie algebras, actual types and Lie teams, the Weyl team, automorphisms, loop algebras and optimum weight representations. The publication additionally discusses particular extra themes, corresponding to Verma modules, Casimirs, tensor items and Clebsch-Gordan coefficients, invariant tensors, subalgebras and branching principles, younger tableaux, spinors, Clifford algebras and supersymmetry, representations on functionality areas, and Hopf algebras and illustration jewelry. a close reference checklist is equipped, and lots of routines and examples in the course of the publication illustrate using Lie algebras in actual actual difficulties. The textual content is written at a degree obtainable to graduate scholars, yet also will supply a complete reference for researchers.
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