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Galois Seminar

Friday, January 25, 2019 - 3:15pm

Bach Nguyen

Temple University


University of Pennsylvania

DRL 4N30

As a noncommutative analog of cluster algebras, quantum cluster algebras were defined by Berenstein and Zelevinsky in 2005. Since then, they have been widely investigated with important applications in the study of canonical bases, combinatorics and representation theory. We define quantum cluster algebras in the setting of roots of unity, and study its properties. In particular, we compute the discriminant of quantum cluster algebras. As examples, we apply the theory to quantum Schubert cells and quantum double Bruhat cells. This is a joint work with Trampel and Yakimov.