Classification of quantum groups and geometrical meaning of the Yang-Baxter equation

Project funded by Swedish Research Council (Project grant), grant 2012-03876_VR. Participating organisations named by the source: University of Gothenburg. Funded amount: SEK 2,229,000, as stated by the source. Runs 2013-01-01 to 2015-12-31. Keywords: Naturvetenskap, Natural Sciences, Matematik, Mathematics, Geometri, Geometry. 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 main aim of the presented project is a classification of Lie bialgebras and quantum groups. Lie bialgebras were defined by V. Drinfeld in 1983. They are closely related to Poisson--Lie groups and Poisson homogeneous spaces. The term "quantum group" often denotes a kind of noncommutative algebra with additional structure that first appeared in the theory of quantum integrable systems, and which was then formalized by Vladimir Drinfel´d and Michio Jimbo as a particular class of Hopf algebras. The first part of the project is devoted to classification of Lie bialgebras and quantum groups related to simple Lie algebras and their extensions, for instance loop algebras. Another very important aim of the project is to find relations between classification of Lie bialgebras and geometry of algebraic curves of genus one. Relations between solutions of the classical Yang-Baxter equation and geometry of elliptic curves were discovered by Polishchuk, who provided a spectacular and impressive application of methods of mirror symmetry. Relations between geometry of other types of the genus one curves and the Yang-Baxter equation will be investigated in this project. Results of the project will be important in applications to integrable models, algebraic geometry and algebraic number theory.

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: The project, funded by the Swedish Research Council, focuses on classifying Lie bialgebras and quantum groups, running from 2013 to 2015 with a budget of SEK 2,229,000. It involves the University of Gothenburg and explores connections to Poisson-Lie groups. Suggested technology pillar: enabling. Generated by AI from the public source text; it may contain errors and the original source is authoritative.