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Quantum groups and cluster algebras both provide frameworks for encoding algebraic and geometric structures arising in representation theory, geometry, and mathematical physics. Quantum groups, as deformations of universal enveloping algebras, capture generalized symmetries with rich categorical and representation-theoretic properties. On the other hand, Cluster algebras, introduced by Fomin and Zelevinsky, appear as important algebraic varieties and reveal properties of them through combinatorial rules. Cluster algebras are essential in the study of canonical bases in diverse settings.
Quantum groups and cluster algebras both provide frameworks for encoding algebraic and geometric structures arising in representation theory, geometry, and mathematical physics. Quantum groups, as deformations of universal enveloping algebras, capture generalized symmetries with rich categorical and representation-theoretic properties. On the other hand, Cluster algebras, introduced by Fomin and Zelevinsky, appear as important algebraic varieties and reveal properties of them through combinatorial rules. Cluster algebras are essential in the study of canonical bases in diverse settings.
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Our team won Bulgarian National Science Fund for research project "Friezes in Algebra, Category Theory, Combinatorics, and Dynamical Systems".
Emine Yıldırım wrote an article for European Mathematical Society Magazine ("The Math Solidarity Platform." Eur. Math. Soc. Mag. 139 (2026), pp. 13–14. DOI 10.4171/MAG/299.)
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