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arXiv · 2606.02202

Quantum groups of Lie colour algebras fulfilling the Cartan-Weyl paradigm

R. B. Zhang
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Abstract

Let Gamma be an additive abelian group with a commutative factor omega. We describe the simple and untwisted affine Lie colour algebras which admit a Cartan - Weyl description. For both classes, we construct the quantised universal enveloping colour algebras, and establish their quasi-triangular Hopf colour algebraic structure. These colour quantum groups generalise the Drinfeld - Jimbo quantum groups, which are recovered when Gamma is trivial. They provide an algebraic foundation for investigations in knot theory and soluble models in statistical mechanics.

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R. B. Zhang. 2026-09-17. Quantum groups of Lie colour algebras fulfilling the Cartan-Weyl paradigm. https://doi.org/10.1016/j.geomphys.2026.106008

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