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- Title
F-Polynomials in Quantum Cluster Algebras.
- Authors
Tran, Thao
- Abstract
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 paper, we define and prove the existence of analogous quantum F-polynomials for quantum cluster algebras. We prove some properties of quantum F-polynomials. In particular, we give a recurrence relation which can be used to compute them. Finally, we compute quantum F-polynomials and g-vectors for a certain class of cluster variables, which includes all cluster variables in type $\mbox{A}_{n}$ quantum cluster algebras.
- Subjects
POLYNOMIALS; ALGEBRA; NONCOMMUTATIVE algebras; MATHEMATICS; MATHEMATICAL variables
- Publication
Algebras & Representation Theory, 2011, Vol 14, Issue 6, p1025
- ISSN
1386-923X
- Publication type
Article
- DOI
10.1007/s10468-010-9226-6