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| Format: | Preprint |
| Published: |
2026
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| Online Access: | https://arxiv.org/abs/2606.02202 |
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| _version_ | 1866913179826651136 |
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| author | Zhang, R. B. |
| author_facet | Zhang, R. B. |
| contents | Let $Γ$ be an additive abelian group equipped with a commutative factor $ω$. We describe the simple Lie colour algebras and the associated untwisted affine Lie colour algebras graded by $Γ$, which fulfil the Cartan-Weyl paradigm. The quantised universal enveloping algebras of these (affine) Lie colour algebras are constructed, which are colour analogues of the Drinfeld-Jimbo quantum groups including the latter as the special case of trivial $Γ$. We develop the quasi-triangular Hopf colour algebraic structure of these ``colour quantum groups'', which has immediate applications in areas such as knot theory and statistical mechanics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2606_02202 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Quantum groups of Lie colour algebras fulfilling Cartan-Weyl paradigm Zhang, R. B. Quantum Algebra 17B75, 17B67, 17B37, 16T05 Let $Γ$ be an additive abelian group equipped with a commutative factor $ω$. We describe the simple Lie colour algebras and the associated untwisted affine Lie colour algebras graded by $Γ$, which fulfil the Cartan-Weyl paradigm. The quantised universal enveloping algebras of these (affine) Lie colour algebras are constructed, which are colour analogues of the Drinfeld-Jimbo quantum groups including the latter as the special case of trivial $Γ$. We develop the quasi-triangular Hopf colour algebraic structure of these ``colour quantum groups'', which has immediate applications in areas such as knot theory and statistical mechanics. |
| title | Quantum groups of Lie colour algebras fulfilling Cartan-Weyl paradigm |
| topic | Quantum Algebra 17B75, 17B67, 17B37, 16T05 |
| url | https://arxiv.org/abs/2606.02202 |