Classification of quantum groups and quantum Poisson homogeneous spaces. Kervaire-Murthy conjectures and fine structure of class groups.

Project funded by Swedish Research Council (Project grant), grant 2008-05166_VR. Participating organisations named by the source: University of Gothenburg. Funded amount: SEK 1,910,000, as stated by the source. Runs 2009-01-01 to 2011-12-31. Keywords: Oklassificerat, Unclassified. Source: OpenAIRE Graph, from the funder's project data (collected by OpenAIRE on 2025-12-04); national funding data, not CORDIS. Abstract given by the source: The present project consists of two parts, which can be linked to each other via studies of double cosets of various Lie groups. The first part deals with quantum groups, which were introduced by Drinfeld in his paper ``Quantum groups´´. No exact definition was given and the notion was illustrated by a number of examples. The examples were deformations of universal enveloping algebras U(L), where L was a Lie bialgebra. Later Drinfeld conjectured that any Lie bialgebra can be quantized in a certain sense (it should be a Hopf algebra over C [[h]). The conjecture was proved in 1996. This justifies the following definition: Quantum group is a quantization of a Lie bialgebra. Now the following problem arises: given a Lie algebra L. Then there exist many Lie bialgebra structures on L. How to quantize all of them? For given L we will get many Hopf algebras. Is there any relation between them? The aim of the present project is to classify all quantum groups, which are quantizations of g[u] and g[u,v]/{uv=1}. Here g is a simple complex finite dimensional Lie algebra and quantum groups related to the algebras above play a crucial role in the theory of integrable models. In the second part of the project I will consider class groups of cyclotomic fields. My aim is to give an explicit description of these groups, which were introduced by Kummer in his proof of Fermat´s Last Theorem (they also have relations with L-functions). The results will answer classical problems in 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 the classification of quantum groups and quantum Poisson homogeneous spaces, running from 2009 to 2011 with a budget of SEK 1,910,000. It involves studies of double cosets of various Lie groups and quantum groups. Suggested technology pillar: enabling. Generated by AI from the public source text; it may contain errors and the original source is authoritative.