Poisson algebras associated to quasi-Hopf algebras
Copyright policy )Poisson algebras associated to quasi-Hopf algebras
We define admissible quasi-Hopf quantized universal enveloping (QHQUE) algebras by h-adic valuation conditions. We show that any QHQUE algebra is twist-equivalent to an admissible one. We prove a related statement: any associator is twist-equivalent to a Lie associator. We attach a quantized formal series algebra to each admissible QHQUE algebra and study the resulting Poisson algebras.
We construct a lift for any Lie quasi-bialgebra with zero cobracket
quasi-Hopf quantized universal enveloping algebras, Mathematics(all), Poisson algebras, quasi-triangular Lie bialgebras, Quantum groups (quantized enveloping algebras) and related deformations, Lie bialgebras; Lie coalgebras, Poisson-Lie groups, quantized formal series algebras, Hopf algebras (associative rings and algebras), quasi-triangular quantized universal enveloping algebras, twists, Lie associators, braidings, quantum Yang-Baxter equation, Mathematics - Quantum Algebra, FOS: Mathematics, Quantum Algebra (math.QA), Geometry and quantization, symplectic methods, Quantum groups and related algebraic methods applied to problems in quantum theory, classical limit
quasi-Hopf quantized universal enveloping algebras, Mathematics(all), Poisson algebras, quasi-triangular Lie bialgebras, Quantum groups (quantized enveloping algebras) and related deformations, Lie bialgebras; Lie coalgebras, Poisson-Lie groups, quantized formal series algebras, Hopf algebras (associative rings and algebras), quasi-triangular quantized universal enveloping algebras, twists, Lie associators, braidings, quantum Yang-Baxter equation, Mathematics - Quantum Algebra, FOS: Mathematics, Quantum Algebra (math.QA), Geometry and quantization, symplectic methods, Quantum groups and related algebraic methods applied to problems in quantum theory, classical limit
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