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Quantum geometry of three-dimensional lattices (Q5853626)

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scientific article; zbMATH DE number 7319530

Language	Label	Description	Also known as
English	Quantum geometry of three-dimensional lattices	scientific article; zbMATH DE number 7319530

Statements

scholarly article

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Quantum geometry of three-dimensional lattices (English)

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Vladimir V. Bazhanov

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Vladimir V. Mangazeev

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Sergey M. Sergeev

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Journal of Statistical Mechanics: Theory and Experiment

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publication date

11 March 2021

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full work available at URL

https://arxiv.org/abs/0801.0129

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MaRDI profile type

MaRDI publication profile

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Some Exact Results for the Many-Body Problem in one Dimension with Repulsive Delta-Function Interaction

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Partition function of the eight-vertex lattice model

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A q-difference analogue of \(U({\mathfrak g})\) and the Yang-Baxter equation

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Infinite conformal symmetry in two-dimensional quantum field theory

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Faddeev-Volkov solution of the Yang-Baxter equation and discrete conformal symmetry

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Exact solution of the Faddeev-Volkov model

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Abelian current algebra and the Virasoro algebra on the lattice

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Variational principles for circle patterns and Koebe’s theorem

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The Yang-Baxter equations and the Zamolodchikov model

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New solvable lattice models in three dimensions

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Star-triangle relation for a three-dimensional model

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SPATIAL SYMMETRY, LOCAL INTEGRABILITY AND TETRAHEDRON EQUATIONS IN THE BAXTER-BAZHANOV MODEL

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Tetrahedral Zamolodchikov algebras corresponding to Baxter's \(L\)- operators

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Functional tetrahedron equation

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Zamolodchikov's tetrahedron equation and hidden structure of quantum groups

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\((Z_ N\times\;)^{n-1}\) generalization of the chiral Potts model

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Generalized chiral Potts models and minimal cyclic representations of \(U_ q (\widehat {\mathfrak gl}(n,C))\)

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Construction of higher-dimensional nonlinear integrable systems and of their solutions

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Algebraic-geometric \(n\)-orthogonal curvilinear coordinate systems and solutions of the associativity equations

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Discrete isothermic surfaces.

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Multidimensional quadrilateral lattices are integrable.

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Classification of integrable equations on quad-graphs. The consistency approach

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Menelaus$apos$ theorem, Clifford configurations and inversive geometry of the Schwarzian KP hierarchy

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The integrable discrete analogues of orthogonal coordinate systems are multi-dimensional circular lattices

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Three–dimensional integrable lattices in Euclidean spaces: conjugacy and orthogonality

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\(\bar \partial\)-reductions of the multidimensional quadrilateral lattice. The multidimensional circular lattice

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On discrete three-dimensional equations associated with the local Yang-Baxter relation

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Lattice and q-difference Darboux-Zakharov-Manakov systems via delta -dressing method

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The symmetric, \(d\)-invariant and Egorov reductions of the quadrilateral lattice

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Classical limit for a 3D lattice spin model.

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Integrable operator representations of \(\mathbb{R}_ q^ 2\), \(X_{q,\gamma}\) and \(SL_ q(2,\mathbb{R})\)

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Discrete Heisenberg-Weyl group and modular group

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Hyperbolic geometry: The first 150 years

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Quantum R matrix for the generalized Toda system

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Trigonometric solutions of triangle equations. Simple Lie superalgebras

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Integrable structure of conformal field theory. II: \(Q\)-operator and DDV equation

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Hidden Grassmann structure in the \(XXZ\) model

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Quantum field theory and the Jones polynomial

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Invariants of 3-manifolds via link polynomials and quantum groups

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State sum invariants of 3-manifolds and quantum \(6j\)-symbols

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A LINK INVARIANT FROM QUANTUM DILOGARITHM

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The colored Jones polynomials and the simplicial volume of a knot

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Generalized volume conjecture and the \(A\)-polynomials: The Neumann-Zagier potential function as a classical limit of the partition function

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Quantization of Teichmüller spaces and the quantum dilogarithm

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A quantum Teichmüller space

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Clebsch-Gordan and Racah-Wigner coefficients for a continuous series of representations of \(\mathcal U_q(\mathfrak{sl}(2,\mathbb R))\)

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Identifiers

zbMATH Open document ID

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10.1088/1742-5468/2008/07/P07004

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Mathematics Subject Classification ID

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zbMATH DE Number

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Sitelinks

Mathematics(1 entry)

mardi Publication:5853626

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