From dynamical quantum groups to integrable structures

Project funded by Swedish Research Council (Project grant), grant 2009-00756_VR. Funded amount: SEK 186,600, as stated by the source. Runs 2009-07-01 to 2010-08-31. Keywords: Oklassificerat, Unclassified. Source: OpenAIRE Graph, from the funder's project data (collected by OpenAIRE on 2025-12-06); national funding data, not CORDIS. Abstract given by the source: The purpose of this research project is to generalize important concepts and constructions for quantum groups to dynamical quantum groups. Dynamical quantum groups have important applications to quantum topology, special functions, representation theory and mathematical physics. Firstly I propose to develop Drinfel´d´s notions of a universal R-matrix and quantum double for dynamical quantum groups. Secondly I aim to generalize Majid´s notion of transmutation to the setting of dynamical quantum groups. The first part of the proposal is expected to lead to the proper algebraic incorporation of so called dynamical R-matrices, which are behind the integrability of the interaction-round-a-face models. The generalization of the quantum double construction then provides an abundance of examples of dynamical quantum groups with universal R-matrices. The second part will lead to quantum dynamical versions of conjugacy classes of Lie groups and an algebraic framework of the dynamical reflection equation. These problems are of great importance from both mathematical and physical point of view. On the one hand, having a quantum double construction for dynamical quantum groups would enable one to find new dynamical R-matrices. On the other hand, the second problem is expected to lead to a much better understanding of quantum dynamical symmetric spaces.

Original source.

Source: OpenAIRE Graph: projects of national funders, OpenAIRE, from the project data of Swedish Research Council. Retrieved 2026-10-28. Licence: Creative Commons Attribution 4.0 (OpenAIRE Graph). Selected metadata, adapted presentation; the publisher's record is authoritative. No endorsement by the source is implied. Licence: Creative Commons Attribution 4.0 (CC BY 4.0).

AI-assisted summary: Project funded by Swedish Research Council, SEK 186,600, 2009-07-01 to 2010-08-31. Aims to generalize quantum groups to dynamical quantum groups, with applications in quantum topology and mathematical physics. Suggested technology pillar: enabling. Generated by AI from the public source text; it may contain errors and the original source is authoritative.