In mathematics, a quantum affine algebra (or affine quantum group) is a Hopf algebra that is a q-deformation of the universal enveloping algebra of an affine Lie algebra. They were introduced independently by and as a special case of their general construction of a quantum group from a Cartan matrix. One of their principal applications has been to the theory of solvable lattice models in quantum statistical mechanics, where the Yang–Baxter equation occurs with a spectral parameter. Combinatorial aspects of the representation theory of quantum affine algebras can be described simply using crystal bases, which correspond to the degenerate case when the deformation parameter q vanishes and the Hamiltonian of the associated lattice model can be explicitly diagonalized.
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| - Álgebra cuántica afín (es)
- Quantum affine algebra (en)
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| - En matemáticas, un álgebra cuántica afín (o grupo afín cuántico) es un que cumple ser una q-deformación del universal de un . Fueron introducidas de forma independiente por y como un caso particular de su construcción general de un de una . Una de sus principales aplicaciones ha sido a la teoría de modelos de red resolubles en , donde la ocurre con un parámetro espectral. Los aspectos combinatorios de la teoría de representación de álgebras cuánticas afines se puede describir simplemente utilizando , lo que se corresponde con el caso degenerado en el que el parámetro de deformación q se cancela y el hamiltoniano del modelo de red asociado no se puede diagonalizar explícitamente. (es)
- In mathematics, a quantum affine algebra (or affine quantum group) is a Hopf algebra that is a q-deformation of the universal enveloping algebra of an affine Lie algebra. They were introduced independently by and as a special case of their general construction of a quantum group from a Cartan matrix. One of their principal applications has been to the theory of solvable lattice models in quantum statistical mechanics, where the Yang–Baxter equation occurs with a spectral parameter. Combinatorial aspects of the representation theory of quantum affine algebras can be described simply using crystal bases, which correspond to the degenerate case when the deformation parameter q vanishes and the Hamiltonian of the associated lattice model can be explicitly diagonalized. (en)
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| - En matemáticas, un álgebra cuántica afín (o grupo afín cuántico) es un que cumple ser una q-deformación del universal de un . Fueron introducidas de forma independiente por y como un caso particular de su construcción general de un de una . Una de sus principales aplicaciones ha sido a la teoría de modelos de red resolubles en , donde la ocurre con un parámetro espectral. Los aspectos combinatorios de la teoría de representación de álgebras cuánticas afines se puede describir simplemente utilizando , lo que se corresponde con el caso degenerado en el que el parámetro de deformación q se cancela y el hamiltoniano del modelo de red asociado no se puede diagonalizar explícitamente. (es)
- In mathematics, a quantum affine algebra (or affine quantum group) is a Hopf algebra that is a q-deformation of the universal enveloping algebra of an affine Lie algebra. They were introduced independently by and as a special case of their general construction of a quantum group from a Cartan matrix. One of their principal applications has been to the theory of solvable lattice models in quantum statistical mechanics, where the Yang–Baxter equation occurs with a spectral parameter. Combinatorial aspects of the representation theory of quantum affine algebras can be described simply using crystal bases, which correspond to the degenerate case when the deformation parameter q vanishes and the Hamiltonian of the associated lattice model can be explicitly diagonalized. (en)
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