The pentagon relation and incidence geometry

DOI10.1063/1.4882285zbMath1295.51004arXiv1108.0944OpenAlexW2095374768WikidataQ104434187 ScholiaQ104434187MaRDI QIDQ5171417

Adam Doliwa, Sergey M. Sergeev

Publication date: 26 July 2014

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

Full work available at URL: https://arxiv.org/abs/1108.0944

zbMATH Keywords

Desargues configurationsWeyl relationsVeblen configurationdynamical pentagon equationquantum pentagon equation

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Commutation relations and statistics as related to quantum mechanics (general) (81S05) Incidence structures embeddable into projective geometries (51A45) Skew fields, division rings (12E15)

Related Items (4)

Non-commutative rational Yang-Baxter maps ⋮ The Coxeter relations and KP map for non-commuting symbols ⋮ Non-commutative birational maps satisfying Zamolodchikov equation, and Desargues lattices ⋮ Non-commutative double-sided continued fractions

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Quantum Teichmüller space from the quantum plane
• The affine Weyl group symmetry of Desargues maps and of the non-commutative Hirota-Miwa system
• The B-quadrilateral lattice, its transformations and the algebro-geometric construction
• The C-(symmetric) quadrilateral lattice, its transformations and the algebro-geometric construction
• Yang-Baxter maps from the discrete BKP equation
• The quantum dilogarithm and representations of quantum cluster varieties
• Classical limits of the SU(2)-invariant solutions of the Yang-Baxter equation
• Poisson Lie groups and pentagonal transformations
• On pentagon, ten-term, and tetrahedron relations
• Poisson-Lie groups. The quantum duality principle and the twisted quantum double
• On the Drinfeld double and the Heisenberg double of a Hopf algebra
• Lax pair for the Adler (lattice Krichever-Novikov) system
• Unitary representations of \(U_{q} (\mathfrak s\mathfrak l(2,\mathbb R))\), the modular double and the multiparticle \(q\)-deformed Toda chain
• Quantization of Teichmüller spaces and the quantum dilogarithm
• Yang-Baxter maps and integrable dynamics
• The symmetric, \(d\)-invariant and Egorov reductions of the quadrilateral lattice
• Lectures on algebraic quantum groups
• On Hirota's difference equations
• Integrable noncommutative equations on quad-graphs. The consistency approach
• Classification of integrable equations on quad-graphs. The consistency approach
• Discrete Heisenberg-Weyl group and modular group
• The integrable discrete analogues of orthogonal coordinate systems are multi-dimensional circular lattices
• Multidimensional quadrilateral lattices are integrable.
• Geometric discretisation of the Toda system.
• An invitation to quantum groups and duality. From Hopf algebras to multiplicative unitaries and beyond
• On discrete three-dimensional equations associated with the local Yang-Baxter relation
• Transformations of quadrilateral lattices
• Classification of Integrable Discrete Equations of Octahedron Type
• Quantum Geometry of 3-Dimensional Lattices and Tetrahedron Equation
• Supertetrahedra and superalgebras
• T-systems andY-systems in integrable systems
• Unitaires multiplicatifs et dualité pour les produits croisés de $\mathrm{C}^*$-algèbres
• A unitary joint eigenfunction transform for the AOs exp(ia±d/dz) + exp(2z/a)
• Yang-Baxter maps and symmetries of integrable equations on quad-graphs
• YANG–BAXTER MAPS AND THE DISCRETE KP HIERARCHY
• Investigating the integrability of the Lyness mappings
• Hyperdeterminants as integrable discrete systems
• Method for Generating Discrete Soliton Equation. III
• Crossed Products and Multiplicative Analogues of Weyl Algebras
• On some unsolved problems in quantum group theory
• On Kronecker limit formula for real quadratic fields
• First order analytic difference equations and integrable quantum systems
• Menelaus$apos$ theorem, Clifford configurations and inversive geometry of the Schwarzian KP hierarchy
• HEISENBERG DOUBLE, PENTAGON EQUATION, STRUCTURE AND CLASSIFICATION OF FINITE-DIMENSIONAL HOPF ALGEBRAS
• Implicit function theorem as a realization of the Lagrange principle. Abnormal points
• QUANTUM EXPONENTIAL FUNCTION
• FROM MULTIPLICATIVE UNITARIES TO QUANTUM GROUPS
• Lattice and q-difference Darboux-Zakharov-Manakov systems via delta -dressing method
• Desargues maps and the Hirota–Miwa equation
• Zamolodchikov's tetrahedron equation and hidden structure of quantum groups
• On Negatons of the Toda Lattice
• Quantization of three-wave equations
• On a non-Abelian Hirota–Miwa equation
• The Historical Development of Algebraic Geometry
• The direct linearisation approach to hierarchies of integrable PDEs in 2 + 1 dimensions: I. Lattice equations and the differential-difference hierarchies
• Quantum geometry of three-dimensional lattices
• Locally compact quantum groups
• Strongly coupled quantum discrete Liouville theory. I: Algebraic approach and duality

This page was built for publication: The pentagon relation and incidence geometry