TRR 358 - Affine Kac–Moody groups: algebra, analysis and arithmetic (Subprojct A05)


Affine Kac-Moody groups and related groups (like loop groups) will be studied from several perspectives. We shall investigate finiteness properties of special linear groups over Laurent polynomials over the ring of integers. We also strive to classify certain maximal Lie orders corresponding to trigonometric solutions of the classical Yang-Baxter equation. In both cases, group actions on affine twin buildings are an essential tool. Such solutions give rise to Lie-Poisson structures on loop groups. The requisite theory of infinite-dimensional Lie-Poisson groups and related Poisson geometry will be developed.

DFG Programme CRC/Transregios

Subproject of TRR 358: Integral Structures in Geometry and Representation Theory

Applicant Institution Universität Bielefeld

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Project duration:
01/2023 - 12/2026
Funded by:
DFG-Datenbank gepris

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Principal Investigators

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Prof. Dr. Helge Glöckner

Infinite-dimensional Analysis and Geometry

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Prof. Dr. Igor Burban


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Kai-Uwe Bux

Universität Bielefeld

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Cooperating Institutions

Universität Bielefeld

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