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.

References in corpus (1)

• Purity for graded potentials and quantum cluster positivity

Cited by in corpus (6)

• Triangular bases in quantum cluster algebras and monoidal categorification conjectures
• Strong positivity for quantum theta bases of quantum cluster algebras
• Dual canonical bases and quantum cluster algebras
• The existence of greedy bases in rank 2 quantum cluster algebras
• Tensor diagrams and Chebyshev polynomials
• Cluster multiplication theorem in the quantum cluster algebra of type $A_2^{(2)}$