Differential calculus on quantized simple Lie groups
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Publication:1182265
DOI10.1007/BF00403543zbMath0753.17020WikidataQ115395032 ScholiaQ115395032MaRDI QIDQ1182265
Publication date: 28 June 1992
Published in: Letters in Mathematical Physics (Search for Journal in Brave)
Quantum groups (quantized enveloping algebras) and related deformations (17B37) Noncommutative topology (46L85) Noncommutative differential geometry (46L87)
Related Items (46)
Hodge star as braided Fourier transform ⋮ Quantization of differential calculi on universal enveloping algebras ⋮ Uq(2) YANG–MILLS THEORY ⋮ Generalized Lie algebras of type An ⋮ More on quantum groups from the quantization point of view ⋮ Classification of bicovariant differential calculi on quantum groups of type \(A, B, C\) and \(D\) ⋮ Classification of differential calculi on Uq(b+), classical limits, and duality ⋮ Classification of bicovariant differential calculi on quantum groups ⋮ Braided Hopf algebras and differential calculus ⋮ Differential calculus on \(ISO_ q(N)\), quantum Poincaré algebra and \(q\)-gravity ⋮ Graded Poisson Lie structures on classical complex Lie groups ⋮ Quantum double and differential calculi ⋮ De Rham complexes of q-analog of general linear group GLq(N) ⋮ Extended reflection equation algebras, the braid group on a handlebody, and associated link polynomials ⋮ A Borel-Weil theorem for the quantum Grassmannians ⋮ Representations of 𝒰h (𝔰𝔲(N) ) derived from quantum flag manifolds ⋮ Quantization of Lie group and algebra of G2 type in the Faddeev–Reshetikhin–Takhtajan approach ⋮ q-deformed Chern characters for quantum groups SUq(N) ⋮ On Poisson–Lie structure on the external algebra of the classical Lie groups ⋮ On Fock-space representations of quantized enveloping algebras related to noncommutative differential geometry ⋮ Differential Hopf algebra structure of the quantum standard complex ⋮ On the noncommutative Riemannian geometry of GLq(n) ⋮ Coherent states for quantum compact groups ⋮ On the algebraic structure of differential calculus on quantum groups ⋮ Differential geometry on linear quantum groups ⋮ Complex quantum groups and their quantum enveloping algebras ⋮ Vector fields on complex quantum groups ⋮ The Hopf algebra of vector fields on complex quantum groups ⋮ A class of bicovariant differential calculi on Hopf algebras ⋮ Quantum groups and free differential algebras in field theory ⋮ Bicovariant calculus in quantum theory and a generalization of the Gauss law. ⋮ Quantum bundle description of quantum projective spaces ⋮ Le langage des espaces et des groupes quantiques. (The language of quantum spaces and quantum groups) ⋮ Complex quantum group, dual algebra and bicovariant differential calculus ⋮ On the biparametric quantum deformation of GL(2)⊗GL(1) ⋮ Remarks on bicovariant differential calculi and exterior Hopf algebras ⋮ Graded Poisson-Lie structures on general linear groups ⋮ Differential Hopf algebras on quantum groups of type A ⋮ Bicovariant differential calculus on quantum groups and wave mechanics ⋮ Classification of bicovariant differential calculi ⋮ A bicovariant differential algebra of a quantum group ⋮ Bicovariant quantum algebras and quantum Lie algebras ⋮ Quantum deformation of BRST algebra ⋮ BRST and anti-BRST operators for quantum linear algebra \(U_q(\text{gl}(N))\) ⋮ Differential calculus on the inhomogeneous quantum groups \(\text{IGL}_ q(n)\) ⋮ Braided Lie algebras and bicovariant differential calculi over co-quasitriangular Hopf algebras
Cites Work
- Differential calculus on quantum spheres
- A q-difference analogue of \(U({\mathfrak g})\) and the Yang-Baxter equation
- Compact matrix pseudogroups
- Twisted \(\text{SU}(2)\) group. An example of a non-commutative differential calculus
- Differential calculus on compact matrix pseudogroups (quantum groups)
- Relating the approaches to quantised algebras and quantum groups
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