A survey on maximal green sequences
arXiv:1904.09247
Abstract
Maximal green sequences appear in the study of Fomin-Zelevinsky's cluster algebras. They are useful for computing refined Donaldson-Thomas invariants, constructing twist automorphisms and proving the existence of theta bases and generic bases. We survey recent progress on their existence and properties and give a representation-theoretic proof of Greg Muller's theorem stating that full subquivers inherit maximal green sequences. In the appendix, Laurent Demonet describes maximal chains of torsion classes in terms of bricks generalizing a theorem by Igusa.
arXiv comment15 pages, submitted to the proceedings of the ICRA 18, Prague, comments welcome; v2: misquotation in section 6 corrected; v3: minor changes, final version; v4: reference to Jiarui Fei's work added, post-final version; v4: formulation of Remark 4.3 corrected; v5: misquotation of Hermes-Igusa's 2019 paper corrected; v5: reference to Kim-Yamazaki's paper added
References in corpus (36)
- Stability structures, motivic Donaldson-Thomas invariants and cluster transformations
- Wall-crossing, Hitchin Systems, and the WKB Approximation
- Cluster structures for 2-Calabi-Yau categories and unipotent groups
- Kac-Moody groups and cluster algebras
- Abelian Current Algebra and the Virasoro Algebra on the Lattice
- N=2 Quantum Field Theories and Their BPS Quivers
- Braids, Walls, and Mirrors
- Newton-Okounkov bodies, cluster duality, and mirror symmetry for Grassmannians
- Wall and Chamber Structure for finite-dimensional Algebras
- The twist for positroid varieties
- Cluster Complexes via Semi-Invariants
- Mutations of group species with potentials and their representations. Applications to cluster algebras
- Quiver mutation and combinatorial DT-invariants
- A compendium on the cluster algebra and quiver package in sage
- Modulated semi-invariants
- On cluster algebras from once punctured closed surfaces
- Stability conditions, -tilting Theory and Maximal Green Sequences
- C-sortable words as green mutation sequences
- Linearity of stability conditions
- Minimal inclusions of torsion classes
- Comments on Exchange Graphs in Cluster Algebras
- Maximal Green Sequences for Cluster Algebras Associated to the n-Torus
- Donaldson-Thomas Transformation of Double Bruhat Cells in Semisimple Lie Groups
- Remarks on lengths of maximal green sequences for quivers of type
- An algebraic approach to Harder-Narasimhan filtrations
- Cluster Structures on Double Bott-Samelson Cells
- Length categories of infinite height
- Donaldson-Thomas Transformation of Grassmannian
- Reddening Sequences for Banff Quivers and the Class
- Uniformly column sign-coherence and the existence of maximal green sequences
- Tensor Product Multiplicities via Upper Cluster Algebras
- Donaldson-Thomas Transformation of Double Bruhat Cells in General Linear Groups
- Maximal green sequences for cluster-tilted algebras of finite representation type
- Stability conditions for affine type A
- The formula for the permutation of mutation sequences in straight orientation
- Maximal green sequences of quivers with multiple edges
Cited by in corpus (9)
- Linearity of stability conditions
- Bruhat inversions in Weyl groups and torsion-free classes over preprojective algebras
- An algebraic approach to Harder-Narasimhan filtrations
- Generic Caldero-Chapoton functions with coefficients and applications to surface cluster algebras
- On maximal green sequences in abelian length categories
- Quivers with analytic potentials
- On maximal green sequence for quivers arising from weighted projective lines
- Jacobian matrices of Y-seed mutations
- Lengths of maximal green sequences for tame path algebras