Dirac operators, Clifford algebras and their quantum analogues

Project funded by Croatian Science Foundation (HRZZ) (Research Projects), grant IP-2025-02-6514. Participating organisations named by the source: Prirodoslovno-matematički fakultet, Zagreb. Funded amount: EUR 191,696, as stated by the source. Runs 2025-12-05 to 2028-12-04. Keywords: Dirac operator, Clifford algebra, Lie algebra, quantum group, Clifford analysis, representation theory. Source: OpenAIRE Graph, from the funder's project data (collected by OpenAIRE on 2026-06-29); national funding data, not CORDIS. Abstract given by the source: This ambitious project focuses on extension of interaction between representation theory, geometry, and analysis. The project is divided into two main parts: (i) Clifford algebras; (ii) Dirac operators. In the first part of the project, we investigate the structureof Clifford algebras associated to symmetric pairs aiming to generalize classical constructions on a quantum level. Our motivation comes from extremely successful applications of Clifford algebras in analysis, geometry, and representation theory. In the second part, we explore the use of algebraic Dirac operators in the study of unitary modules. Finally, we aim to generalize constructions of Dirac operators to the case of quantum groups, quantum symmetric pairs, and the framework of quantum Clifford analysis. Further related research tasks bring together the representation theory of Lie groups, and classical and noncommutative geometries. The project subteams provide unique complementary top experience in the touched hot international topics, including their wide cooperating international network.

Original source.

Source: OpenAIRE Graph: projects of national funders, OpenAIRE, from the project data of Croatian Science Foundation (HRZZ). Retrieved 2026-10-22. 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 "Dirac operators, Clifford algebras and their quantum analogues" is funded by the Croatian Science Foundation with a grant of EUR 191,696, running from December 5, 2025, to December 4, 2028. It focuses on the interaction between representation theory, geometry, and analysis. Suggested technology pillar: enabling. Generated by AI from the public source text; it may contain errors and the original source is authoritative.