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Questions about algebraic structures known as quantum groups, and their categories of representations. Quasitriangular Hopf algebras and their Drinfel'd twists, triangular Hopf algebras, $C^\star$ quantum groups, h-adic quantum groups, various semisimplified categories at roots of unity which are called "quantum groups", bicrossproduct quantum groups, and quantum groups coming from braided tensor categories.
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Does there exist any "quantum Lie algebra" embeded into the quantum enveloping algebra U_q(g)?
Two seemingly easy to read references are given in the papers 'An introduction to Quantum Lie Algebras' by Delius which is available here: http://arxiv.org/pdf/q-alg/9605026v1.pdf and 'Quantum Lie Alg …