Compare triangular bases of acyclic quantum cluster algebras
Quantum Algebra
2020-04-28 v2 Representation Theory
Abstract
Given a quantum cluster algebra, we show that its triangular bases defined by Berenstein and Zelevinsky and those defined by the author are the same for the seeds associated with acyclic quivers. This result implies that the Berenstein-Zelevinsky's basis contains all the quantum cluster monomials. We also give an easy proof that the two bases are the same for the seeds associated with bipartite skew-symmetrizable matrices.
Keywords
Cite
@article{arxiv.1606.05604,
title = {Compare triangular bases of acyclic quantum cluster algebras},
author = {Fan Qin},
journal= {arXiv preprint arXiv:1606.05604},
year = {2020}
}
Comments
18 pages; minor correction; the proof of Lemma 3.2.1 corrected