• DOI:10.1007/s00220-019-03660-9
• Corpus ID: 208650775

q-Independence of the Jimbo–Drinfeld Quantization

@article{Giselsson2018qIndependenceOT,
  title={q-Independence of the Jimbo–Drinfeld Quantization},
  author={Olof Giselsson},
  journal={Communications in Mathematical Physics},
  year={2018},
  volume={376},
  pages={1737 - 1765}
}

• Olof Giselsson
• Published 5 November 2018
• Materials Science
• Communications in Mathematical Physics

Let G\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathrm {G}}$$\end{document} be a connected semi-simple compact Lie group and for 0<q<1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$0<q<1$$\end{document}, let (C[G]q,Δq)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$({\mathbb {C}}[\mathrm {G]_q},\varDelta _q)$$\end{document} be the Jimbo–Drinfeld q-deformation of G\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathrm {G}}$$\end{document}. We show that the C∗\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$C^*$$\end{document}-completions of C[G]q\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathrm {C}[\mathrm {G]_q}$$\end{document} are isomorphic for all values of q. Moreover, these isomorphisms are equivariant with respect to the right-actions of the maximal torus.