Bases for cluster algebras from surfaces Page 1 COMPOSITIO MATHEMATICA Bases for
cluster algebras from surfaces Gregg Musiker, Ralf Schiffler and Lauren Williams …

We consider the quantum cluster algebras which are injective-reachable and introduce a
triangular basis in every seed. We prove that, under some initial conditions, there exists a …

The exchange graph of a cluster algebra encodes the combinatorics of mutations of clusters.
Through the recent" categorifications" of cluster algebras using representation theory one …

Linear independence of cluster monomials for skew-symmetric cluster algebras Page 1
COMPOSITIO MATHEMATICA Linear independence of cluster monomials for skew-symmetric …

Inspired by recent work of Geiss–Leclerc–Schröer, we use Hom-finite cluster categories to
give a good candidate set for a basis of (upper) cluster algebras with coefficients arising …

The skein algebra of a marked surface, possibly with punctures, admits the basis of (tagged)
bracelet elements constructed by Fock-Goncharov and Musiker-Schiffler-Williams. As a …

In a series of works, Geiss, Leclerc, and Schröer defined the cluster algebra structure on the
coordinate ring C [N (w)] of the unipotent subgroup, associated with a Weyl group element …

The rings of SL (V) invariants of configurations of vectors and linear forms in a finite-
dimensional complex vector space V were explicitly described by Hermann Weyl in the …

The homogeneous coordinate ring of the Grassmannian Gr k, n has a cluster structure
defined in terms of planar diagrams known as Postnikov diagrams. The cluster …

It is known that many (upper) cluster algebras possess different kinds of good bases which
contain the cluster monomials and are parametrized by the tropical points of cluster Poisson …