Quantized braided groups

DOI10.1063/1.530523zbMath0810.17007arXivhep-th/9210152OpenAlexW1784891489MaRDI QIDQ4314238

Ladislav Hlavatý

Publication date: 17 April 1995

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

Full work available at URL: https://arxiv.org/abs/hep-th/9210152

zbMATH Keywords

quantum groupsbraided groupreflection equationtransmutation

Mathematics Subject Classification ID

Related Items (17)

Generalized sine-Gordon models and quantum braided groups ⋮ Spectral extension of the quantum group cotangent bundle ⋮ Quantum matrix algebras of BMW type: structure of the characteristic subalgebra ⋮ Algebraic framework for quantization of nonultralocal models ⋮ Nonstandard quantum groups and superization ⋮ On Fock-space representations of quantized enveloping algebras related to noncommutative differential geometry ⋮ Graded reflection equations and the one-dimensional Bariev open chain. ⋮ Tropical limit of matrix solitons and entwining Yang-Baxter maps ⋮ Measurement of `closeness' and distinguishability of the quantum states in Yang-Baxter systems ⋮ Quantized braided linear algebras relating to quantized braided groups ⋮ Differential calculuses on the quantized braided groups ⋮ Nonstandard comodules for quantum matrix bialgebras ⋮ SOLUTION OF THE YANG–BAXTER SYSTEM FOR QUANTUM DOUBLES ⋮ Classification of Quantized Braided Groups in the Dimension 2 ⋮ Quantum matrix algebras of the \(\text{GL}(m|n)\) type: the structure and spectral parameterization of the characteristic subalgebra ⋮ Ultralocal solutions for quantum integrable non-ultralocal models ⋮ Dynamics of the quantum coherence under the concatenation of Yang-Baxter matrix

Cites Work

• Classical r-matrix and exchange algebra in WZNW and Toda theories
• A Hopf star-algebra of polynomials on the quantum \(SL(2,\mathbb{R})\) for a `unitary' \(R\)-matrix
• Quantum matrices in two dimensions
• Braided groups and algebraic quantum field theories
• Multiparameter quantum groups and twisted quasitriangular Hopf algebras
• QUANTUM LIE SUPERALGEBRAS AND “NON-STANDARD” BRAID GROUP REPRESENTATIONS
• A REMARK ON QUANTUM SUPERGROUPS
• Unusual solutions to the Yang-Baxter equation
• Two-dimensional quantum spaces corresponding to solutions of the Yang-Baxter equations
• Examples of braided groups and braided matrices
• Yang-Baxter matrices and differential calculi on quantum hyperplanes
• Quantum and braided linear algebra
• Transmutation theory and rank for quantum braided groups

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