The non-commutative \(A_1T\)-system and its positive Laurent property

DOI10.1007/s00220-014-2223-6zbMath1320.82008arXiv1402.2851OpenAlexW3103136861MaRDI QIDQ2339175

Philippe Di Francesco

Publication date: 31 March 2015

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1402.2851

zbMATH Keywords

Bethe Ansatz solution\(T\)-systemspositive Laurent propertynon-commutative Laurent property

Mathematics Subject Classification ID

Noncommutative dynamical systems (46L55) Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20)

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Cites Work

• \(T\)-systems, networks and dimers
• The solution of the quantum \(A_1\) \(T\)-system for arbitrary boundary
• Friezes
• A short proof of Kontsevich's cluster conjecture.
• Non-commutative integrability, paths and quasi-determinants
• Proof of the Kontsevich non-commutative cluster positivity conjecture.
• \(Q\)-systems as cluster algebras. II: Cartan matrix of finite type and the polynomial property
• Quasideterminants. I
• Quasideterminants
• T-systems with boundaries from network solutions
• Quantum cluster algebras.
• FUNCTIONAL RELATIONS IN SOLVABLE LATTICE MODELS I: FUNCTIONAL RELATIONS AND REPRESENTATION THEORY
• Cluster algebras I: Foundations
• Discrete Non-commutative Integrability: Proof of a Conjecture by M. Kontsevich
• Proof of a positivity conjecture of M. Kontsevich on non-commutative cluster variables

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