Killing Form on Quasitriangular Hopf Algebras and Quantum Lie Algebras

Paul Watts

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arXiv · q-alg/9505027

Killing Form on Quasitriangular Hopf Algebras and Quantum Lie Algebras

Paul Watts

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Abstract

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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Paul Watts. 1995-05-23. Killing Form on Quasitriangular Hopf Algebras and Quantum Lie Algebras. https://arxiv.org/abs/q-alg/9505027

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