English

Quantum $SL^+(N,\mathbb{R})$ as a locally compact quantum group

Quantum Algebra 2025-12-29 v1 Operator Algebras

Abstract

We construct the first examples of purely continuous, qq-deformed Lie type locally compact quantum groups in higher rank. They arise from Drinfeld-Jimbo quantization, at unimodular deformation parameter, of the totally positive part of higher rank split real Lie groups in type AA. Our techniques are based on quantum cluster theory, in particular as developed through the work of Fock and Goncharov.

Keywords

Cite

@article{arxiv.2512.21579,
  title  = {Quantum $SL^+(N,\mathbb{R})$ as a locally compact quantum group},
  author = {K. De Commer and G. Schrader and A. Shapiro and C. Voigt},
  journal= {arXiv preprint arXiv:2512.21579},
  year   = {2025}
}

Comments

112 pages, 21 figures

R2 v1 2026-07-01T08:40:46.276Z