Bases of the quantum cluster algebra of the Kronecker quiver
AbstractWe construct bar-invariant $\mathbb{Z}[q^{ \pm \tfrac{1}
{2}} ]
$-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.