CONVERGENT TWIST DEFORMATIONS

Speaker(s)

MICHAEL HEINS

Affiliation

Technische Universiteit Delft, Netherlands

Language of the talk

English

Date

April 29, 2026, 5:15 p.m.

Information about the event

IMPAN - Room 405 & zoom

Title in Polish

CONVERGENT TWIST DEFORMATIONS

Seminar

North Atlantic Noncommutative Geometry Seminar

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We discuss a functorial framework for the convergence of Drinfeld's Universal Deformation Formula on spaces of analytic vectors. Algebraically, the principal idea is that a Drinfeld twist induces formal deformations of any associative algebra on which the underlying Lie algebra acts by derivations. Equipping the representation space with a locally convex topology, we overcome the formal character of this deformation, which allows us to plug in a complex number for the formal parameter to obtain power series convergent within our topology. This is achieved by matching an equicontinuity condition for the action of the components of the twist with the order of analytic vectors of the representation. Finally, we demonstrate the effectiveness of our theory by applying it to the explicit Drinfeld twists constructed by Giaquinto and Zhang, and determine concrete spaces of analytic vectors. This is joint work with Chiara Esposito and Stefan Waldmann.

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