Bases of the quantum cluster algebra of the Kronecker quiver

Authors
Ding, Ming Xu, Fan
Citation
Ding, Ming et Xu, Fan, Bases of the quantum cluster algebra of the Kronecker quiver, Acta mathematica Sinica. English series (Print) , 28(6), 2012, pp. 1169-1178
Journal title
Acta mathematica Sinica. English series (Print) → ACNP
ISSN journal
14398516
Volume
28
Issue
6
Year of publication
2012
Pages
1169 - 1178
Database
ACNP
SICI code
Abstract
We construct bar-invariant Z[q±12]-bases of the quantum cluster algebra of Kronecker quiver which are quantum analogues of the canonical basis, semicanonical basis and dual semicanonical basis of the corresponding cluster algebra. As a byproduct, we prove positivity of the elements in these bases.