title: Greedy bases in rank 2 quantum cluster algebras.
abstract: We identify a quantum lift of the greedy basis for rank 2 coefficient-free cluster algebras. Our main result is that our construction does not depend on the choice of initial cluster, that it builds all cluster monomials, and that it produces bar-invariant elements. We also present several conjectures related to this quantum greedy basis and the triangular basis of Berenstein and Zelevinsky.
authors: Department of Mathematics, Wayne State University, Detroit, MI 48202;
authors: Kyungyong
authors: K
authors: Lee
authors: Department of Mathematics and Statistics, Oakland University, Rochester, MI 48309; and.
authors: Li
authors: L
authors: Li
authors: Department of Mathematics, Northeastern University, Boston, MA 02115 d.rupel@neu.edu.
authors: Dylan
authors: D
authors: Rupel
authors: Department of Mathematics, Northeastern University, Boston, MA 02115.
authors: Andrei
authors: A
authors: Zelevinsky
keywords: standard monomial basis; triangular basis