Poisson-Lie \(T\)-duality and Bianchi type algebras

DOI10.1016/S0370-2693(99)00571-7zbMath0963.17014arXivhep-th/9903152OpenAlexW2102829297WikidataQ126807127 ScholiaQ126807127MaRDI QIDQ5934554

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Publication date: 7 May 2001

Published in: Physics Letters. B (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/hep-th/9903152

zbMATH Keywords

\(\sigma\)-models with Poisson-Lie symmetryBianchi bialgebrasDrinfeld doubles

Mathematics Subject Classification ID

Quantum groups (quantized enveloping algebras) and related deformations (17B37) Model quantum field theories (81T10) Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, (W)-algebras and other current algebras and their representations (81R10) Lie bialgebras; Lie coalgebras (17B62)

Related Items (16)

CLASSIFICATION OF SIX-DIMENSIONAL REAL DRINFELD DOUBLES ⋮ Lie superbialgebra structures on the Lie superalgebra C3+A and deformation of related integrable Hamiltonian systems ⋮ Generalised fluxes, Yang-Baxter deformations and the O\((d,d)\) structure of non-abelian \(T\)-duality ⋮ (4+1)-DIMENSIONAL HOMOGENEOUS ANISOTROPIC STRING COSMOLOGICAL MODELS ⋮ CLASSIFICATION OF POISSON–LIE T-DUAL MODELS WITH TWO-DIMENSIONAL TARGETS ⋮ Classical \(r\)-matrices of two- and three-dimensional Lie superbialgebras and their Poisson-Lie supergroups ⋮ One-loop renormalizability of all 2-dimensional Poisson-Lie \(\sigma\)-models ⋮ Classification of real low-dimensional Jacobi (generalized)–Lie bialgebras ⋮ Jacobi-Lie symmetry and Jacobi-Lie T-dual sigma models on group manifolds ⋮ Dressing cosets revisited ⋮ Classification of four-dimensional real Lie bialgebras of symplectic type and their Poisson-Lie groups ⋮ Poisson-Lie duality in the string effective action ⋮ The Poincaré group as a Drinfel’d double ⋮ Some compatible Poisson structures and integrable bi-Hamiltonian systems on four dimensional and nilpotent six dimensional symplectic real Lie groups ⋮ Classification of two and three dimensional Lie superbialgebras ⋮ Classification of four and six dimensional Drinfel’d superdoubles

Cites Work

• Unnamed Item
• Symplectic structures associated to Lie-Poisson groups
• \(T\)-duality and two-loop renormalization flows
• Poisson-Lie \(T\)-duality and loop groups of Drinfeld doubles.
• Quantum Poisson-Lie \(T\)-duality and WZNW model
• Empty space-times admitting a three parameter group of motions

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