The Drinfeld double gl(n) \oplus t_n

Abstract

The two isomorphic Borel subalgebras of gl(n), realized on upper and lower triangular matrices, allow us to consider the gl(n) \opus t_n algebra as a self-dual Drinfeld double. Compatibility conditions impose the choice of an orthonormal basis in the Cartan subalgebra and fix the basis of gl(n). A natural Lie bialgebra structure on gl(n) is obtained, that offers a new perspective for its standard quantum deformation.

8 pages

References in corpus (18)

• Dual Non-Abelian Duality and the Drinfeld Double
• Poisson-Lie T-duality and Loop Groups of Drinfeld Doubles
• Poisson-Lie T-plurality
• The Quantum Double in Integrable Quantum Field Theory
• Making electromagnetic wavelets II: Spheroidal shell antennas
• Topological field theory and the quantum double of SU(2)
• Classification of 6-dimensional real Drinfeld doubles
• An introduction to quantized Lie groups and algebras
• A Closed Expression for the Universal R-Matrix in a Non-Standard Quantum Double
• Classification of Poisson-Lie T-dual models with two-dimensional targets
• Three dimensional quantum algebras: a Cartan-like point of view
• Quantization of Drinfel'd doubles
• On modular spaces of semisimple Drinfeld doubles
• Deformations of Multiparameter Quantum gl(N)
• Deformed boson algebras and the quantum double construction
• BRST Algebra Quantum Double and Quantization of the Proper Time Cotangent Bundle
• Exotic Quantum Double,Its Universal R-matrix And Their Representations
• Quantum double of Heisenberg-Weyl algebra, its universal R-matrix and their representations

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• From Quantum Universal Enveloping Algebras to Quantum Algebras
• Bases in Lie and Quantum Algebras