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q-Independence of the Jimbo-Drinfeld Quantization

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Olof Giselsson

Quantum Algebra · Submitted 5 Nov 2018

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim We show that the $C^*$-completions of $\mathrm{C}[\mathrm{G]_q}$ are isomorphic for all values of $q$.

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arXiv ID1811.01864 (version 2)
Pith IDSH2BXLBE, Pith's permanent record of this paper and its review
CitationOlof Giselsson. "q-Independence of the Jimbo-Drinfeld Quantization." arXiv:1811.01864 (2018). https://pith.science/paper/SH2BXLBE
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,022 input tokens.

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arXiv listing abstract v2. Results and the main claim are underlined; .

Let $\mathrm G$ be a connected semi-simple compact Lie group and for $0<q<1$, let $(\mathbb{C}[\mathrm{G]_q}],\Delta_q)$ be the Jimbo-Drinfeld $q$-deformation of $\mathrm G$. We show that the $C^*$-completions of $\mathrm{C}[\mathrm{G]_q}$ are isomorphic for all values of $q$. Moreover, these isomorphisms are equivariant with respect to the right-action of the maximal torus.

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#sentencerolethe authors' own workstates the main conclusionstrength
s0 Let $\mathrm G$ be a connected semi-simple compact Lie group and for $0<q<1$, let $(\mathbb{C}[\mathrm{G]_q}],\Delta_q)$ be the Jimbo-Drinfeld $q$-deformation of $\mathrm G$. background 1.00 0.09 0.02 asserted 0.72
s1 We show that the $C^*$-completions of $\mathrm{C}[\mathrm{G]_q}$ are isomorphic for all values of $q$. result 0.99 0.96 0.91 asserted 1.00
s2 Moreover, these isomorphisms are equivariant with respect to the right-action of the maximal torus. result 1.00 0.90 0.12 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 1.00.

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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

Let $\mathrm G$ be a connected semi-simple compact Lie group and for $0<q<1$, let $(\mathbb{C}[\mathrm{G]_q}],\Delta_q)$ be the Jimbo-Drinfeld $q$-deformation of $\mathrm G$. We show that the $C^*$-completions of $\mathrm{C}[\mathrm{G]_q}$ are isomorphic for all values of $q$. Moreover, these isomorphisms are equivariant with respect to the right-action of the maximal torus.

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