Cluster Realization of Positive Representations of a Split Real Quantum Borel Subalgebra

@article{Ip2017ClusterRO,
  title={Cluster Realization of Positive Representations of a Split Real Quantum Borel Subalgebra},
  author={Ivan C. H. Ip},
  journal={Theoretical and Mathematical Physics},
  year={2017},
  volume={198},
  pages={215-238}
}
  • I. Ip
  • Published 30 November 2017
  • Mathematics
  • Theoretical and Mathematical Physics
Abstractour previous work, we studied positive representations of split real quantum groups $$\mathcal{U}_{q\widetilde{q}}(\mathfrak{g}_\mathbb{R})$$Uqq~(gR) restricted to their Borel part and showed that they are closed under taking tensor products. But the tensor product decomposition was only constructed abstractly using the GNS representation of a C*-algebraic version of the Drinfeld–Jimbo quantum groups. Here, using the recently discovered cluster realization of quantum groups, we write… 

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Cluster realization of Uq(g)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal {U}_q(\mathfrak {g})$$\end{docume

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For each simple Lie algebra g\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs}

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Cluster realization of $$\mathcal {U}_q(\mathfrak {g})$$Uq(g) and factorizations of the universal R-matrix

  • I. Ip
  • Mathematics
    Selecta Mathematica
  • 2018
For each simple Lie algebra $$\mathfrak {g}$$g, we construct an algebra embedding of the quantum group $$\mathcal {U}_q(\mathfrak {g})$$Uq(g) into certain quantum torus algebra $$\mathcal

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