Quantum current algebras and their representation theory

Project funded by Croatian Science Foundation (HRZZ) (Installation Research Projects), grant UIP-2019-04-8488. Participating organisations named by the source: Prirodoslovno-matematički fakultet, Zagreb; University of Zagreb, Faculty of Science. Funded amount: EUR 193,644, as stated by the source. Runs 2020-01-01 to 2024-12-31. Keywords: quantum vertex algebras, quantum affine algebras, principal subspaces, affine Lie algebras, Rogers-Ramanujan identities, Hopf algebroids. Source: OpenAIRE Graph, from the funder's project data (collected by OpenAIRE on 2026-07-23); national funding data, not CORDIS. Abstract given by the source: Quantum current algebras represent a fundamental conection between two important areas of modern algebra, quantum groups and quantum vertex algebras. More precisely, they occur in the realizations of certain classes of quantum groups while, on the other hand, they play a central role in the construction of quantum vertex algebras. The proposed project will establish the first research group in the field of quantum vertex algebras in Croatia. The group will primarily focus on the development of the theory of algebras of quantum currents. The main goal is to establish a connection between theories of representations of certain classes of quantum vertex algebras and the corresponding quantum groups. This will result in new and important methods and tools whose wide range of applications in different areas of mathematics we plan to study in detail. For example, using the concept of a quasi-module, we obtain new results in the theory of reflection algebras, which are used in mathematical physics to describe integrable systems with boundary conditions. Furthermore, by introducing and studying the notion of principal subspace for certain classes of modules of quantum current algebras, we obtain new examples of simple quantum vertex algebras, as well as a new environment for studying Rogers-Ramanujan-type combinatorial identities. The group brings together the research forces of members dealing with complementary fields, the theory of quantum vertex algebras, the theory of representations of affine Lie algebras and the theory of Hopf algebras, which are key to the successful implementation of the project. The doctoral student will benefit greatly from such a research environment because he will gain valuable experience in these areas. Mastering the most modern methods and participating in the development of new tools will prepare him to successfully follow his own research directions in any of them in the future.

Original source.

Source: OpenAIRE Graph: projects of national funders, OpenAIRE, from the project data of Croatian Science Foundation (HRZZ). 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 "Quantum current algebras and their representation theory" is funded by the Croatian Science Foundation with a grant of EUR 193,644, running from January 1, 2020, to December 31, 2024. It aims to establish a research group in Croatia focused on quantum vertex algebras. Suggested technology pillar: enabling. Generated by AI from the public source text; it may contain errors and the original source is authoritative.