Quantum Braided Groups

Abstract

A new type of algebras that represent a generalization of both quantum groups and braided groups is defined. These algebras are given by a pair of solutions of the Yang--Baxter equation that satisfy some additional conditions. Several examples are presented.

10 pages, LATeX, In any related matters please contact [email protected]

References in corpus (3)

• The complete solution to the constant quantum Yang-Baxter equation in two dimensions
• Quantum and Braided Linear Algebra
• Constant Solutions of Reflection Equations and Quantum Groups

Cited by in corpus (25)

• Introduction to Braided Geometry and $q$-Minkowski Space
• Spectral extension of the quantum group cotangent bundle
• Exact conserved quantities on the cylinder I: conformal case
• A braided Yang-Baxter Algebra in a Theory of two coupled Lattice Quantum KdV: algebraic properties and ABA representations
• Orthogonal and Symplectic Quantum Matrix Algebras and Cayley-Hamilton Theorem for them
• From the braided to the usual Yang-Baxter relation
• Exact conserved quantities on the cylinder II: off-critical case
• The GL(m|n) type quantum matrix algebras II: the structure of the characteristic subalgebra and its spectral parameterization
• Commuting quantum traces for quadratic algebras
• Yang-Baxter systems, solutions and applications
• Algebraic Framework for Quantization of Nonultralocal Models
• On Fock Space Representations of quantized Enveloping Algebras related to Non-Commutative Differential Geometry
• Action in Hamiltonian Models Constructed by Yang-Baxter Equation: Entanglement and Measures of Correlation
• Commuting quantum traces: the case of reflection algebras
• Solution of a Yang-Baxter system
• Quantum Braided PoincarÉ Group
• Generalized sine-Gordon models and quantum braided groups
• Some Comments on Bosonisation and Biproducts
• Tropical limit of matrix solitons and entwining Yang-Baxter maps
• Schur Polynomials and the Yang-Baxter equation
• Ultralocal solutions for quantum integrable nonultralocal models
• Squared Hopf algebras and reconstruction theorems
• On braided FRT-construction
• Solution of Constant Yang-Baxter System in the Dimension Two
• Non-Commutative Corepresentations of Quantum Groups