Noncommutative marked surfaces

DOI10.1016/j.aim.2018.02.014zbMath1395.14001arXiv1510.02628OpenAlexW2963437007MaRDI QIDQ1705484

Arkady Berenstein, Vladimir S. Retakh

Publication date: 15 March 2018

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1510.02628

zbMATH Keywords

triangulationLaurent phenomenonmarked surfacenon-commutatice cluster algebra

Mathematics Subject Classification ID

Noncommutative algebraic geometry (14A22) Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Noncommutative geometry (à la Connes) (58B34) Cluster algebras (13F60)

Related Items

Friezes, weak friezes, and T-paths, Birational rowmotion on a rectangle over a noncommutative ring, Noncommutative marked surfaces, New expansion formulas for cluster algebras from surfaces, An expansion formula for decorated super-Teichmüller spaces, Algebras of quasi-Plücker coordinates are Koszul, Noncommutative Catalan numbers, An expansion formula for type \(A\) and Kronecker quantum cluster algebras, An expansion formula for quantum cluster algebras from unpunctured triangulated surfaces, Symplectic groups over noncommutative algebras, Positivity for quantum cluster algebras from unpunctured orbifolds

Cites Work

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• Cluster expansion formulas and perfect matchings
• Non-commutative integrability, paths and quasi-determinants
• Cluster algebras and triangulated orbifolds
• Cluster algebras and triangulated surfaces. I: Cluster complexes
• Rigidity of polyhedral surfaces. II.
• A cluster expansion formula (\(A_{n}\) case)
• The decorated Teichmüller space of punctured surfaces
• Quasideterminants. I
• A new foundation for the theory of relations
• An embedding of the group algebra of a torsion-free one-relator group in a field
• A theory of noncommutative determinants and characteristic functions of graphs
• Noncommutative marked surfaces
• Cluster algebras. III: Upper bounds and double Bruhat cells.
• Quasideterminants
• Determinants of matrices over noncommutative rings
• The non-commutative \(A_1T\)-system and its positive Laurent property
• Moduli spaces of local systems and higher Teichmüller theory
• The Group Rings that are Semifirs
• Cluster Algebras and Triangulated Surfaces Part II: Lambda Lengths
• Free Associative Algebras
• Quivers with relations arising from clusters (𝐴_{𝑛} case)