5 mars 2019: 1 événement

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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