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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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Cite

BibTeXRIS
BibTeX
@misc{zhang2026quantum,
  title = {{Quantum groups of Lie colour algebras fulfilling the Cartan-Weyl paradigm}},
  author = {R. B. Zhang},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2606.02202},
  eprint = {2606.02202},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2606.02202},
}
RIS
TY  - UNPB
TI  - Quantum groups of Lie colour algebras fulfilling the Cartan-Weyl paradigm
AU  - R. B. Zhang
PY  - 2026
DA  - 2026/09/17
PB  - arXiv
DO  - 10.48550/arxiv.2606.02202
UR  - https://arxiv.org/abs/2606.02202
AB  - 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.
ER  -