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Banach Poisson–Lie Group Structure on \( \operatorname {U}( \mathcal {H})\)

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Geometric Methods in Physics XXXIX (WGMP 2022)

Part of the book series: Trends in Mathematics ((TM))

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Abstract

We construct a Banach Poisson–Lie group structure on the unitary group of a separable complex Hilbert space.

This research was partially supported by joint National Science Centre, Poland (number 2020/01/Y/ST1/00123) and Fonds zur Förderung der wissenschaftlichen Forschung, Austria (number I 5015-N) grant “Banach Poisson–Lie groups and integrable systems.”

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Author information

Authors and Affiliations

  1. UMR CNRS 8524, UFR de Mathématiques, Laboratoire Paul Painlevé, Villeneuve d’Ascq Cedex, France

    Alice Barbora Tumpach

  2. Institut CNRS Pauli, UMI CNRS 2842, Wien, Austria

    Alice Barbora Tumpach

  3. University of Białystok, Białystok, Poland

    Tomasz Goliński

Authors
  1. Alice Barbora Tumpach
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  2. Tomasz Goliński
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Corresponding author

Correspondence to Alice Barbora Tumpach .

Editor information

Editors and Affiliations

  1. Departamento de Física, CINVESTAV, Ciudad de México, Mexico

    Piotr Kielanowski

  2. Faculty of Mathematics, University of Białystok, Białystok, Poland

    Alina Dobrogowska

  3. Departments of Mathematics, Physics, Learning & Teaching, Rutgers University, New Brunswick, NJ, USA

    Gerald A. Goldin

  4. Faculty of Mathematics, University of Białystok, Białystok, Poland

    Tomasz Goliński

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Tumpach, A.B., Goliński, T. (2023). Banach Poisson–Lie Group Structure on \( \operatorname {U}( \mathcal {H})\). In: Kielanowski, P., Dobrogowska, A., Goldin, G.A., Goliński, T. (eds) Geometric Methods in Physics XXXIX. WGMP 2022. Trends in Mathematics. Birkhäuser, Cham. https://doi.org/10.1007/978-3-031-30284-8_22

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