Communications in Contemporary Mathematics, ISSN 0219-1997, 12/2019, Volume 21, Issue 8, p. 1850069

We construct three families of vertex algebras along with their modules from appropriate vertex Lie algebras, using the constructions in [Vertex Lie algebra,...

Bakas-Block algebra | vertex Lie algebra | polynomial Virasoro algebra | vertex tensor category | β γ -system | Strongly graded vertex algebra | C 1 A -cofiniteness condition | INVARIANCE | MATHEMATICS, APPLIED | REPRESENTATIONS | EQUATIONS | MATHEMATICS | C-1(A)-cofiniteness condition | SYSTEMS | QUASIFINITE MODULES | beta gamma-system | Algebra

Bakas-Block algebra | vertex Lie algebra | polynomial Virasoro algebra | vertex tensor category | β γ -system | Strongly graded vertex algebra | C 1 A -cofiniteness condition | INVARIANCE | MATHEMATICS, APPLIED | REPRESENTATIONS | EQUATIONS | MATHEMATICS | C-1(A)-cofiniteness condition | SYSTEMS | QUASIFINITE MODULES | beta gamma-system | Algebra

Journal Article

Communications in Contemporary Mathematics, ISSN 0219-1997, 04/2017, Volume 19, Issue 2, p. 1650009

We derive certain systems of differential equations for matrix elements of products and iterates of logarithmic intertwining operators among strongly graded...

Logarithmic intertwining operators | Strongly graded vertex algebra | cofiniteness condition | Differential equations | Logarithmic tensor category | MATHEMATICS | logarithmic tensor category | MATHEMATICS, APPLIED | logarithmic intertwining operators | C-1-cofiniteness condition | differential equations | Algebra

Logarithmic intertwining operators | Strongly graded vertex algebra | cofiniteness condition | Differential equations | Logarithmic tensor category | MATHEMATICS | logarithmic tensor category | MATHEMATICS, APPLIED | logarithmic intertwining operators | C-1-cofiniteness condition | differential equations | Algebra

Journal Article

International Journal of Mathematics, ISSN 0129-167X, 05/2016, Volume 27, Issue 5, p. 1650046

We construct a family of vertex algebras associated to the affine Lie algebra of polynomial current algebras of finite-dimensional abelian Lie algebras, along...

strongly graded vertex algebras | logarithmic modules | logarithmic tensor categories | Polynomial current algebras | MATHEMATICS | INTERTWINING-OPERATORS | Algebra

strongly graded vertex algebras | logarithmic modules | logarithmic tensor categories | Polynomial current algebras | MATHEMATICS | INTERTWINING-OPERATORS | Algebra

Journal Article

Annales Henri Poincaré, ISSN 1424-0637, 1/2015, Volume 16, Issue 1, pp. 113 - 161

We present a construction of non-equilibrium steady states in one-dimensional quantum critical systems carrying energy and charge fluxes. This construction is...

Gibbs State | Mathematical Methods in Physics | Theoretical, Mathematical and Computational Physics | Topological Defect | Vertex Operator | Quantum Physics | Partial Algebra | Vertex Operator Algebra | Dynamical Systems and Ergodic Theory | Classical and Quantum Gravitation, Relativity Theory | Physics | Elementary Particles, Quantum Field Theory | INVARIANCE | STATISTICAL-MECHANICS | PHYSICS, MULTIDISCIPLINARY | LIQUID | SYSTEMS | PHYSICS, MATHEMATICAL | COUNTING STATISTICS | PHYSICS, PARTICLES & FIELDS | Sects | Reservoirs

Gibbs State | Mathematical Methods in Physics | Theoretical, Mathematical and Computational Physics | Topological Defect | Vertex Operator | Quantum Physics | Partial Algebra | Vertex Operator Algebra | Dynamical Systems and Ergodic Theory | Classical and Quantum Gravitation, Relativity Theory | Physics | Elementary Particles, Quantum Field Theory | INVARIANCE | STATISTICAL-MECHANICS | PHYSICS, MULTIDISCIPLINARY | LIQUID | SYSTEMS | PHYSICS, MATHEMATICAL | COUNTING STATISTICS | PHYSICS, PARTICLES & FIELDS | Sects | Reservoirs

Journal Article

Communications in Mathematical Physics, ISSN 0010-3616, 8/2015, Volume 337, Issue 3, pp. 1053 - 1076

We introduce a twisted version of the Heisenberg double, constructed from a twisted Hopf algebra and a twisted pairing. We state a Stone–von Neumann type...

Quantum Physics | Statistical Physics, Dynamical Systems and Complexity | Mathematical Physics | Classical and Quantum Gravitation, Relativity Theory | Theoretical, Mathematical and Computational Physics | Physics | ALGEBRAS | VERTEX REPRESENTATIONS | PHYSICS, MATHEMATICAL | CATEGORIFICATION | Algebra

Quantum Physics | Statistical Physics, Dynamical Systems and Complexity | Mathematical Physics | Classical and Quantum Gravitation, Relativity Theory | Theoretical, Mathematical and Computational Physics | Physics | ALGEBRAS | VERTEX REPRESENTATIONS | PHYSICS, MATHEMATICAL | CATEGORIFICATION | Algebra

Journal Article

Journal of Statistical Mechanics: Theory and Experiment, ISSN 1742-5468, 02/2005, Volume 2005, Issue 2, pp. P02007 - 110

We present an 'algebraic treatment' of the analytical Bethe ansatz. For this purpose, we introduce abstract monodromy and transfer matrices which provide an...

Integrable spin chains (vertex models) | Algebraic structures of integrable models | Symmetries of integrable models | Quantum integrability (Bethe ansatz) | algebraic structures of integrable models | LOW-LYING EXCITATIONS | SPIN-1/2 XXZ CHAIN | EVOLUTION-EQUATIONS | PHYSICS, MATHEMATICAL | quantum integrability (Bethe ansatz) | symmetries of integrable models | QUANTUM-FIELD-THEORY | FACTORIZED S-MATRIX | REFLECTION EQUATION | ISOTROPIC HEISENBERG CHAIN | MECHANICS | integrable spin chains (vertex models) | HALF-LINE | INTEGRABLE MODEL | NONDIAGONAL BOUNDARY TERMS

Integrable spin chains (vertex models) | Algebraic structures of integrable models | Symmetries of integrable models | Quantum integrability (Bethe ansatz) | algebraic structures of integrable models | LOW-LYING EXCITATIONS | SPIN-1/2 XXZ CHAIN | EVOLUTION-EQUATIONS | PHYSICS, MATHEMATICAL | quantum integrability (Bethe ansatz) | symmetries of integrable models | QUANTUM-FIELD-THEORY | FACTORIZED S-MATRIX | REFLECTION EQUATION | ISOTROPIC HEISENBERG CHAIN | MECHANICS | integrable spin chains (vertex models) | HALF-LINE | INTEGRABLE MODEL | NONDIAGONAL BOUNDARY TERMS

Journal Article

Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8121, 06/2008, Volume 41, Issue 25, p. 255204

The centrally extended superalgebra psu(2 vertical bar 2) x R-3 was shown to play an important role for the integrable structures of the one-dimensional...

DILATATION OPERATOR | INTEGRABLE SPIN CHAIN | VERTEX MODEL | T-J MODELS | REPRESENTATIONS | PHYSICS, MULTIDISCIPLINARY | ALGEBRAIC BETHE-ANSATZ | STRONGLY CORRELATED ELECTRONS | EXACTLY SOLVABLE MODEL | LIE SUPERALGEBRA GL(2/2) | PHYSICS, MATHEMATICAL | GAUGE

DILATATION OPERATOR | INTEGRABLE SPIN CHAIN | VERTEX MODEL | T-J MODELS | REPRESENTATIONS | PHYSICS, MULTIDISCIPLINARY | ALGEBRAIC BETHE-ANSATZ | STRONGLY CORRELATED ELECTRONS | EXACTLY SOLVABLE MODEL | LIE SUPERALGEBRA GL(2/2) | PHYSICS, MATHEMATICAL | GAUGE

Journal Article

Nuclear Physics, Section B, ISSN 0550-3213, 09/2014, Volume 886, Issue C, pp. 436 - 482

Instead of studying anyon condensation in various concrete models, we take a bootstrap approach by considering an abstract situation, in which an anyon...

SUBFACTORS | ALPHA-INDUCTION | ALGEBRAS | MODULAR INVARIANTS | CONSTRUCTION | PHYSICS, PARTICLES & FIELDS | Analysis | Algebra | Mathematics - Quantum Algebra | High Energy Physics | Nuclear and High Energy Physics | Theory | Condensed Matter - Strongly Correlated Electrons | Nuclear and particle physics. Atomic energy. Radioactivity | Mathematics - Category Theory

SUBFACTORS | ALPHA-INDUCTION | ALGEBRAS | MODULAR INVARIANTS | CONSTRUCTION | PHYSICS, PARTICLES & FIELDS | Analysis | Algebra | Mathematics - Quantum Algebra | High Energy Physics | Nuclear and High Energy Physics | Theory | Condensed Matter - Strongly Correlated Electrons | Nuclear and particle physics. Atomic energy. Radioactivity | Mathematics - Category Theory

Journal Article

Transformation Groups, ISSN 1083-4362, 12/2017, Volume 22, Issue 4, pp. 1005 - 1029

We investigate the representation theory of domestic group schemes G $$ \mathcal{G} $$ over an algebraically closed field of characteristic p > 2. We present...

Topological Groups, Lie Groups | Mathematics | Algebra | LIE-ALGEBRAS | MATHEMATICS | QUIVERS | PRODUCTS | STRONGLY GRADED RINGS | HOPF GALOIS EXTENSIONS

Topological Groups, Lie Groups | Mathematics | Algebra | LIE-ALGEBRAS | MATHEMATICS | QUIVERS | PRODUCTS | STRONGLY GRADED RINGS | HOPF GALOIS EXTENSIONS

Journal Article

Nuclear Physics, Section B, ISSN 0550-3213, 1999, Volume 552, Issue 3, pp. 707 - 726

We investigate the algebraic structure of a recently proposed integrable t-J model with impurities. Three forms of the Bethe ansatz equations are presented...

Integrable spin chains | Graded algebras | Yang-Baxter algebra | Algebraic Bethe ansatz | Algebraic bethe ansatz | Yang-baxter algebra | algebraic Bethe ansatz | IRREPS | integrable spin chains | BAND | HUBBARD-MODEL | BETHE-ANSATZ | CHAIN | COMBINING DIFFERENT REPRESENTATIONS | ONE DIMENSION | SYSTEMS | LATTICE | graded algebras | PHYSICS, PARTICLES & FIELDS | Physics - Mesoscale and Nanoscale Physics | Physics - Quantum Gases | Physics - Disordered Systems and Neural Networks | Physics - Other Condensed Matter | Physics - Strongly Correlated Electrons | Physics - Soft Condensed Matter | Physics - Superconductivity | Physics - Statistical Mechanics | Physics - Materials Science

Integrable spin chains | Graded algebras | Yang-Baxter algebra | Algebraic Bethe ansatz | Algebraic bethe ansatz | Yang-baxter algebra | algebraic Bethe ansatz | IRREPS | integrable spin chains | BAND | HUBBARD-MODEL | BETHE-ANSATZ | CHAIN | COMBINING DIFFERENT REPRESENTATIONS | ONE DIMENSION | SYSTEMS | LATTICE | graded algebras | PHYSICS, PARTICLES & FIELDS | Physics - Mesoscale and Nanoscale Physics | Physics - Quantum Gases | Physics - Disordered Systems and Neural Networks | Physics - Other Condensed Matter | Physics - Strongly Correlated Electrons | Physics - Soft Condensed Matter | Physics - Superconductivity | Physics - Statistical Mechanics | Physics - Materials Science

Journal Article

Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8121, 07/2008, Volume 41, Issue 29, p. 295202

We present in a unified and detailed way the nested Bethe ansatz for closed spin chains based on Y(gl (n)), Y(gl (m|n)), (U) over cap (q)(gl (n)) or (U) over...

ANALOG | PHYSICS, MULTIDISCIPLINARY | QUANTUM | ALGEBRA | TRANSFER-MATRICES | EQUATIONS | FINITE-DIMENSIONAL REPRESENTATIONS | MODEL | PHYSICS, MATHEMATICAL | IRREDUCIBLE REPRESENTATIONS

ANALOG | PHYSICS, MULTIDISCIPLINARY | QUANTUM | ALGEBRA | TRANSFER-MATRICES | EQUATIONS | FINITE-DIMENSIONAL REPRESENTATIONS | MODEL | PHYSICS, MATHEMATICAL | IRREDUCIBLE REPRESENTATIONS

Journal Article

Journal of Statistical Mechanics: Theory and Experiment, ISSN 1742-5468, 07/2013, Volume 2013, Issue 7, pp. P07009 - 19

The small polaron with generic, nondiagonal boundary terms is investigated within the framework of quantum integrability. The fusion hierarchy of the transfer...

integrable spin chains (vertex models) | solvable lattice models | quantum integrability (Bethe ansatz) | MECHANICS | XXZ SPIN CHAIN | OPERATOR | T-J MODEL | PHYSICS, MATHEMATICAL | EQUATION | Hierarchies | Mathematical analysis | Transfer matrices | Eigenvalues | Mathematical models | Spectra | Boundaries | Polarons

integrable spin chains (vertex models) | solvable lattice models | quantum integrability (Bethe ansatz) | MECHANICS | XXZ SPIN CHAIN | OPERATOR | T-J MODEL | PHYSICS, MATHEMATICAL | EQUATION | Hierarchies | Mathematical analysis | Transfer matrices | Eigenvalues | Mathematical models | Spectra | Boundaries | Polarons

Journal Article

Nuclear Physics, Section B, ISSN 0550-3213, 1998, Volume 516, Issue 3, pp. 588 - 602

A general graded reflection equation algebra is proposed and the corresponding boundary quantum inverse scattering method is formulated. The formalism is...

QUANTUM SUPERSYMMETRY | SUPERCONDUCTIVITY | ALGEBRAIC BETHE-ANSATZ | MATRICES | VERTEX | EXACTLY SOLVABLE MODEL | SYSTEMS | OPEN SPIN CHAINS | PHYSICS, PARTICLES & FIELDS

QUANTUM SUPERSYMMETRY | SUPERCONDUCTIVITY | ALGEBRAIC BETHE-ANSATZ | MATRICES | VERTEX | EXACTLY SOLVABLE MODEL | SYSTEMS | OPEN SPIN CHAINS | PHYSICS, PARTICLES & FIELDS

Journal Article

Nuclear Physics, Section B, ISSN 0550-3213, 2004, Volume 687, Issue 3, pp. 257 - 278

We formulate the Bethe ansatz equations for the open super-spin chain based on the super Yangian of osp( M|2 n) and with diagonal boundary conditions. We then...

SYMMETRY | FUSION | MASSIVE THIRRING MODEL | QUANTUM-SYSTEMS | T-J MODEL | PHYSICS, NUCLEAR | INTEGRABLE MODEL | SPECTRUM | SUPERSYMMETRIC U MODEL | OPEN-BOUNDARY CONDITIONS | PHYSICS, PARTICLES & FIELDS | Quantum Algebra | Mathematics | Mathematical Physics | High Energy Physics - Theory | Physics

SYMMETRY | FUSION | MASSIVE THIRRING MODEL | QUANTUM-SYSTEMS | T-J MODEL | PHYSICS, NUCLEAR | INTEGRABLE MODEL | SPECTRUM | SUPERSYMMETRIC U MODEL | OPEN-BOUNDARY CONDITIONS | PHYSICS, PARTICLES & FIELDS | Quantum Algebra | Mathematics | Mathematical Physics | High Energy Physics - Theory | Physics

Journal Article

Communications in Mathematical Physics, ISSN 0010-3616, 05/2006, Volume 264, Issue 1, pp. 87 - 114

We construct the Drinfeld twists (or factorizing F-matrices) of the supersymmetric model associated with quantum superalgebra U-q(gl(m vertical bar n)), and...

CHAIN | EXACTLY SOLVABLE MODEL | PHYSICS, MATHEMATICAL | CORRELATED ELECTRONS

CHAIN | EXACTLY SOLVABLE MODEL | PHYSICS, MATHEMATICAL | CORRELATED ELECTRONS

Journal Article

Mathematical Notes, ISSN 0001-4346, 12/2009, Volume 86, Issue 5, pp. 665 - 681

The so-called λ-Koszul algebra and λ-Koszul module are introduced. We give different equivalent descriptions of the λ-Koszul algebra in terms of its minimal...

λ-Koszul algebras ( modules ) | module over a graded algebra | Mathematics, general | Yoneda Ext- algebras | Mathematics | A ∞ -algebras | Lie algebra | ( strongly ) weakly λ-Koszul | algebras | Module over a graded algebra | Yoneda Ext-algebras | (strongly) weakly λ-Koszul | λ-Koszul algebras (modules) | MATHEMATICS | KOSZUL ALGEBRAS | lambda-Koszul algebras (modules) | A(infinity)-algebras | (strongly) weakly lambda-Koszul

λ-Koszul algebras ( modules ) | module over a graded algebra | Mathematics, general | Yoneda Ext- algebras | Mathematics | A ∞ -algebras | Lie algebra | ( strongly ) weakly λ-Koszul | algebras | Module over a graded algebra | Yoneda Ext-algebras | (strongly) weakly λ-Koszul | λ-Koszul algebras (modules) | MATHEMATICS | KOSZUL ALGEBRAS | lambda-Koszul algebras (modules) | A(infinity)-algebras | (strongly) weakly lambda-Koszul

Journal Article

Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8121, 05/2009, Volume 42, Issue 20, pp. 205203 - 205203 (35)

We present in a unified and detailed way the nested Bethe ansatz for open spin chains based on Y(gl(n)), Y(gl(m|n)), (U) over cap (q)(gl(n)) or (U) over cap...

REPRESENTATIONS | ANALOG | PHYSICS, MULTIDISCIPLINARY | QUANTUM | TRANSFER-MATRICES | VERTEX | SPECTRUM | MODEL | PHYSICS, MATHEMATICAL | Mathematical Physics | Mathematics | Physics

REPRESENTATIONS | ANALOG | PHYSICS, MULTIDISCIPLINARY | QUANTUM | TRANSFER-MATRICES | VERTEX | SPECTRUM | MODEL | PHYSICS, MATHEMATICAL | Mathematical Physics | Mathematics | Physics

Journal Article

Journal of Mathematical Physics, ISSN 0022-2488, 02/2007, Volume 48, Issue 2, pp. 023504 - 023504-12

By means of the Drinfeld twists, we derive the determinant representations of the partition functions for the g l ( 1 ∣ 1 ) and g l ( 2 ∣ 1 ) supersymmetric...

T-J MODEL | 6-VERTEX MODEL | PHYSICS, MATHEMATICAL | ALGEBRAIC BETHE-ANSATZ | MATRIX MODEL | PHYSICS OF ELEMENTARY PARTICLES AND FIELDS | SUPERSYMMETRY | PARTITION FUNCTIONS | LIE GROUPS | DOMAIN STRUCTURE | BOUNDARY CONDITIONS

T-J MODEL | 6-VERTEX MODEL | PHYSICS, MATHEMATICAL | ALGEBRAIC BETHE-ANSATZ | MATRIX MODEL | PHYSICS OF ELEMENTARY PARTICLES AND FIELDS | SUPERSYMMETRY | PARTITION FUNCTIONS | LIE GROUPS | DOMAIN STRUCTURE | BOUNDARY CONDITIONS

Journal Article

Communications in Mathematical Physics, ISSN 0010-3616, 1/2018, Volume 357, Issue 1, pp. 295 - 317

We show that the Hilbert space formed from a block spin renormalization construction of a cyclic quantum spin chain (based on the Temperley–Lieb algebra) does...

Quantum Physics | Mathematical Physics | Classical and Quantum Gravitation, Relativity Theory | Theoretical, Mathematical and Computational Physics | Complex Systems | Physics | MODELS | PHYSICS, MATHEMATICAL | Algebra

Quantum Physics | Mathematical Physics | Classical and Quantum Gravitation, Relativity Theory | Theoretical, Mathematical and Computational Physics | Complex Systems | Physics | MODELS | PHYSICS, MATHEMATICAL | Algebra

Journal Article

Communications in Algebra, ISSN 0092-7872, 12/2019, Volume 47, Issue 12, pp. 5303 - 5316

We introduce the concept of t-spread monomials and t-spread strongly stable ideals. These concepts are a natural generalization of strongly stable and...

stretching operator | strongly stable ideals | Alexander dual | generic initial ideals | Betti numbers

stretching operator | strongly stable ideals | Alexander dual | generic initial ideals | Betti numbers

Journal Article

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