2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/153399The 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 $\uea{su}{2}$.LaTeX file, 43 pages, no figures, uses "mssymb.tex" macrosQuantum AlgebraHigh Energy Physics - Theorytext