Killing Form on Quasitriangular Hopf Algebras and Quantum Lie Algebras

Details Killing Form on Quasitriangular Hopf Algebras and Quantum Lie Algebras Killing Form on Quasitriangular Hopf Algebras and Quantum Lie Algebras

1995-05-23

arxiv.org/abs/q-alg/9505027v1

Physics

High Energy Physics

High Energy Physics - Theory

LaTeX file, 43 pages, no figures, uses "mssymb.tex" macros

Scientific paper

The basics of quasitriangular Hopf algebras and quantum Lie algebras are briefly reviewed, and it is shown that their properties allow the introduction of a Killing form. For quantum Lie algebras, this leads to the definitions of a Killing metric and quadratic casimir. The specific case of $\uea{su}{N}$ is examined in detail, where it is shown that many of the classical results are reproduced, and explicit calculations to illustrate the conclusions are presented for $\uea{su}{2}$.

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