Maximal Green Sequences for Certain Triangle Products

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Maximal Green Sequences for Certain Triangle Products
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2021
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English

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Bernhard Keller introduced maximal green sequences as a combinatorial tool for computing refined Donaldson-Thomas invariants in the framework of cluster algebras. Maximal green sequences furthermore can be used to prove the existence of nice bases of cluster algebras and play a prominent role in the work on the full Fock-Goncharov conjecture due to Gross-Hacking-Keel-Kontsevich. In Physics, maximal green sequences appear in the computation of spectra of BPS states. We report on joint work with Gleb Koshevoy introducing maximal green sequences for certain triangle products of quivers. As an application we comment on the consequences regarding the full Fock-Goncharov conjecture for double Bruhat cells.
Classical physics Trail Functional (mathematics) Group action Divisor Multiplication sign Element (mathematics) Product (business) Power (physics) Wave packet Vortex Mathematics Exclusive or Forest Squeeze theorem Arrow of time Körper <Algebra> Algebra Cluster sampling Combinatorics Social class Rhombus Process (computing) Consistency Expression Computability Infinity Maxima and minima Lattice (order) Radical (chemistry) Wave Musical ensemble Figurate number Cycle (graph theory) Arithmetic progression Family
Point (geometry) Standard error Group action Building Vapor barrier Divisor Multiplication sign Ultraviolet photoelectron spectroscopy Sheaf (mathematics) Theory 2 (number) Wave packet Product (business) Power (physics) Green's function Cuboid Modulform Arrow of time Social class Physical system Scaling (geometry) Process (computing) Military base Consistency Expression Projective plane Computability Algebraic structure Maxima and minima Cartesian coordinate system Sequence Entire function Connected space Category of being Universe (mathematics) Quantum Right angle Musical ensemble Game theory Identical particles
Rule of inference Random number Link (knot theory) Observational study Multiplication sign Lemma (mathematics) Range (statistics) Open set Mortality rate Sequence Product (business) Frobenius normal form Category of being Mathematics Roundness (object) Positional notation Musical ensemble Discrepancy theory Maß <Mathematik> Directed graph Spacetime Social class
Point (geometry) Pulse (signal processing) Multiplication sign Peg solitaire 10 (number) Thomas Kuhn Product (business) 2 (number) Different (Kate Ryan album) Well-formed formula Operator (mathematics) Green's function Quilt Cuboid Modulform Energy level Arrow of time Monster group Maß <Mathematik> Mathematical optimization Social class Physical system Newton's law of universal gravitation Rule of inference Multiplication Link (knot theory) Process (computing) Consistency Projective plane Sampling (statistics) Algebraic structure Maxima and minima Sequence Repeating decimal Inclusion map Category of being Maxwell's demon Optics Moving average Musical ensemble Directed graph Valuation using multiples
Trail Complex (psychology) Random number Functional (mathematics) Greatest element Link (knot theory) Polymorphism (materials science) Divisor Orientation (vector space) Blind spot (vehicle) Consistency Forcing (mathematics) Projective plane Sampling (statistics) Maxima and minima Water vapor Line (geometry) Product (business) Casting (performing arts) Circle Game theory Musical ensemble Directed graph
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