Laboratoire de Mathématiques de Besançon - UMR 6623 CNRS

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5 mars 2019: 1 événement

  • Séminaire d’Analyse Fonctionnelle

    Mardi 5 mars 13:45-15:00 - Oleg Aristov - Moscou

    Duality for Hopf holomorphically finitely generated algebras

    Résumé : Inspired by the duality theory of locally compact
    quantum groups we discuss a class of topological Hopf algebras
    that can be considered as algebras of ’holomorphic functions on
    quantum complex Lie groups’. A Hopf holomorphically finitely
    generated (HFG) algebra is introduced as a topological Hopf
    algebra that is a quotient of Taylor’s algebra of free entire
    functions. For every Hopf HFG algebra $H$, the dual topological
    Hopf algebra $H^\circ$ can be defined. We talk over conditions,
    under which $H^\circ$ is HFG.
    The natural commutative example of a Hopf HFG algebra is
    $\mathcalO(G)$, the algebra of holomorphic functions on a
    complex Lie group $G$. It is shown, under the assumption that $G$
    is connected, that $\mathcalO(G)^\circ\circ\cong
    \mathcalO(G)$ iff $G$ is linear, i.e., admits a faithful
    finite-dimensional holomorphic representation.

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