Andrei V. Zelevinsky
Gordana G. Todorov, Jerzy M. Weyman, Arkady
Date of Award
Doctor of Philosophy
Department or Academic Unit
College of Arts and Sciences. Department of Mathematics
mathematics, cluster algebras, combinatorics
F-polynomials and g-vectors were defined by Fomin and Zelevinsky to give a formula which expresses cluster variables in a cluster algebra in terms of the initial cluster data. A quantum cluster algebra is a certain noncommutative deformation of a cluster algebra. In this thesis, we define and prove the existence of analogous quantum F -polynomials for quantum cluster algebras. We compute quantum F-polynomials and g-vectors for a certain class of cluster variables, which includes all cluster variables in type A quantum cluster algebras. Finally, we give formulas for F-polynomials and quantum F-polynomials in classical types when the initial exchange matrix is acyclic.
Tran, Thao, "Quantum F-polynomials in the theory of cluster algebras" (2010). Mathematics Dissertations. Paper 14. http://hdl.handle.net/2047/d20000263
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