Book Review: Lecture notes on cluster algebras

DOI10.1090/bull/1514zbMath1332.00028OpenAlexW2321411449MaRDI QIDQ2797793

Ralf Schiffler

Publication date: 31 March 2016

Published in: Bulletin of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/bull/1514

Mathematics Subject Classification ID

(n)-dimensional polytopes (52B11) Grassmannians, Schubert varieties, flag manifolds (14M15) Poisson algebras (17B63) Research exposition (monographs, survey articles) pertaining to commutative algebra (13-02) External book reviews (00A17) Cluster algebras (13F60) Root systems (17B22) Combinatorial aspects of commutative algebra (05E40)

Cites Work

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• Skew-symmetric cluster algebras of finite mutation type
• Snake graph calculus and cluster algebras from surfaces. II: Self-crossing snake graphs
• Quiver varieties and cluster algebras
• Positivity for cluster algebras from surfaces
• Cluster categories for algebras of global dimension 2 and quivers with potential.
• Cluster algebras and quantum affine algebras
• Cluster algebras and triangulated surfaces. I: Cluster complexes
• Cluster algebras. II: Finite type classification
• Cluster algebras and Weil-Petersson forms
• The periodicity conjecture for pairs of Dynkin diagrams
• Positivity for cluster algebras
• Greedy elements in rank 2 cluster algebras
• Snake graph calculus and cluster algebras from surfaces
• From triangulated categories to cluster algebras
• Cluster algebras as Hall algebras of quiver representations.
• Moduli spaces of local systems and higher Teichmüller theory
• Tilting theory and cluster combinatorics.
• Rigid modules over preprojective algebras.
• Cluster algebras I: Foundations
• On cluster algebras from unpunctured surfaces with one marked point
• Triangular Bases in Quantum Cluster Algebras
• Cluster algebras via cluster categories with infinite-dimensional morphism spaces
• Generic bases for cluster algebras and the Chamber Ansatz
• Canonical bases for cluster algebras
• GRASSMANNIANS AND CLUSTER ALGEBRAS
• Cluster-tilted algebras
• Canonical Bases Arising from Quantized Enveloping Algebras
• Quivers with potentials and their representations II: Applications to cluster algebras
• Bases for cluster algebras from surfaces
• Matrix Formulae and Skein Relations for Cluster Algebras from Surfaces
• -tilting theory
• Cluster-tilted algebras as trivial extensions
• Quivers with relations arising from clusters (𝐴_{𝑛} case)

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