Introduction to Cluster Algebras. Chapters 1-3

Abstract

This is a preliminary draft of Chapters 1-3 of our forthcoming textbook "Introduction to Cluster Algebras." This installment contains: Chapter 1. Total positivity Chapter 2. Mutations of quivers and matrices Chapter 3. Clusters and seeds

73 pages. v5: minor editorial changes

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• Toric Duality as Seiberg Duality and Brane Diamonds
• Kac-Moody groups and cluster algebras
• An introduction to the dimer model
• Weak Separation and Plabic Graphs
• Cluster algebras of finite type and positive symmetrizable matrices
• Locally acyclic cluster algebras
• Dual Teichmuller and lamination spaces
• KP solitons, total positivity, and cluster algebras
• Laurent Polynomials and Superintegrable Maps
• Plabic graphs and zonotopal tilings
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• Webs on surfaces, rings of invariants, and clusters
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Cited by in corpus (34)

• Cluster algebras for Feynman integrals
• Algebraic branch points at all loop orders from positive kinematics and wall crossing
• The Berenstein-Zelevinsky quantum cluster algebra conjecture
• Morsifications and mutations
• Cluster structures in Schubert varieties in the Grassmannian
• Immersed two-spheres and SYZ with Application to Grassmannians
• Total positivity of some polynomial matrices that enumerate labeled trees and forests, I. Forests of rooted labeled trees
• Cluster structures and subfans in scattering diagrams
• Factoriality and class groups of cluster algebras
• Weave Realizability for D-type
• Enumerative properties of Grid-Associahedra
• Lagrangian fillings for Legendrian links of affine type
• Gradient flows, adjoint orbits, and the topology of totally nonnegative flag varieties
• Cyclic symmetry loci in Grasssmannians
• Lagrangian Fillings in A-type and their Kalman Loop Orbits
• Parametrizations of $k$-Nonnegative Matrices: Cluster Algebras and $k$-Positivity Tests
• Theta functions and quiver Grassmannians
• Root of unity quantum cluster algebras and discriminants
• Periodicities in cluster algebras and cluster automorphism groups
• Symplectic Frieze Patterns
• An Introduction to Supersymmetric Cluster Algebras
• From frieze patterns to cluster categories
• Deformation Theory for Finite Cluster Complexes
• Dual canonical bases for unipotent groups and base affine spaces
• Root of unity quantum cluster algebras and Cayley-Hamilton algebras
• Cluster Duality for Lagrangian and Orthogonal Grassmannians
• On folded cluster patterns of affine type
• A note on cluster automorphism groups
• On webs, polylogarithms and cluster algebras
• A Lattice Isomorphism Theorem for Cluster Groups of Mutation-Dynkin Type $A_n$
• Positive integer solutions to $(x+y{)}^2+(y+z{)}^2+(z+x{)}^2=12xyz$
• Combinatorics of $\mathcal{X}$-variables in finite type cluster algebras
• Difference equations arising from cluster algebras
• Okamoto's symmetry on the representation space of the sixth Painlevé equation