Witt and Virasoro algebras as Lie bialgebras

DOI10.1016/0022-4049(93)90116-BzbMath0786.17015WikidataQ115364416 ScholiaQ115364416MaRDI QIDQ686112

Earl J. Taft

Publication date: 8 November 1993

Published in: Journal of Pure and Applied Algebra (Search for Journal in Brave)

zbMATH Keywords

Witt algebraVirasoro algebralinearly recursive sequencesclassical Yang-Baxter equationtriangular Lie bialgebra

Mathematics Subject Classification ID

Related Items (51)

Quantizations of generalized-Witt algebra and of Jacobson-Witt algebra in the modular case ⋮ Lie bialgebra structures on the deformative Schrödinger-Virasoro algebras ⋮ Quantizations of the Witt algebra and of simple Lie algebras in characteristic \(p\) ⋮ Lie bialgebras of generalized Witt type ⋮ Dual Lie Bialgebra Structures of Twisted Schrödinger-Virasoro Type ⋮ Quantization of Lie Algebras of Generalized Weyl Type ⋮ Classification of all Poisson-Lie structures on an infinite-dimensional jet group ⋮ Lie bialgebra structures on derivation Lie algebra over quantum tori ⋮ Lie super-bialgebra structures on the Ramond \(N = 2\) super-Virasoro algebra ⋮ Lie bialgebras of generalized Virasoro-like type ⋮ Dual Lie bialgebra structures of Poisson types ⋮ Lie Bialgebra Structures on Lie Algebras of Generalized Weyl Type ⋮ Lie super-bialgebra structures on the two dimensional supersymmetric Galilean conformal algebra ⋮ The deformed twisted Heisenberg–Virasoro type Lie bialgebra ⋮ Lie bialgebra structures on the extended affine Lie algebra \(\widetilde {\mathfrak {sl}_2(\mathbb C_q)}\) ⋮ Schrödinger-Virasoro type Lie bialgebra: a twisted case ⋮ Lie super-bialgebra structures on the Lie superalgebra of Witt type ⋮ Unnamed Item ⋮ Quantization of generalized Virasoro-like algebras ⋮ Classical Yang-Baxter equation and low-dimensional triangular Lie bialgebras ⋮ The strongly symmetric elements and solutions of Yang-Baxter equation ⋮ \(\kappa\)-deformed BMS symmetry ⋮ Lie Bialgebra Structures on the Centerless W-Algebra W(2,2) ⋮ Hamiltonian type Lie bialgebras ⋮ Lie bialgebras of a family of Lie algebras of Block type ⋮ Lie super-bialgebra structures on super \(\mathcal{W}\)-algebra \(\mathcal{SW}(\frac{3}{2}, \frac{3}{2})\) ⋮ On Lie and associative duals ⋮ Drinfel'd Twist Deformations of the Super-Virasoro Algebras ⋮ Lie bialgebra structures on the twisted Heisenberg-Virasoro algebra ⋮ Twists and quantizations of Cartan type \(S\) Lie algebras ⋮ Lie Super-bialgebra Structures on Generalized Ramond N=2 Super-Virasoro Algebras ⋮ Quantizations of the \(W\)-algebra \(W(2,2)\) ⋮ Lie Bialgebras of Generalized WITT Type, II ⋮ Unnamed Item ⋮ Lie bialgebra structures on the Schrödinger–Virasoro Lie algebra ⋮ Poisson–Lie structures on infinite-dimensional jet groups and quantum groups related to them ⋮ Classical \(\mathbb{R}\)-matrices for vertex operator algebras ⋮ Lie Bialgebra Structures on the q-Analog Virasoro-Like Algebras ⋮ Double Hom-associative algebra and double Hom-Lie bialgebra ⋮ Lie Bialgebra Structures on Lie Algebras of Block Type ⋮ Lie Bialgebra Structures on the Extended Schrödinger-Virasoro Lie Algebra ⋮ Lie super-bialgebra structures on a class of generalized super W-algebra L ⋮ Lie bialgebra structures on generalized loop Schrödinger-Virasoro algebras ⋮ Classification of the Lie bialgebra structures on the Witt and Virasoro algebras ⋮ Lie super-bialgebra structures on super-Virasoro algebra ⋮ Existence of triangular Lie bialgebra structures ⋮ Is quantum simulation of turbulence within reach? ⋮ Lie super-bialgebra structures on the N = 2 super-BMS₃ algebra ⋮ Dual Lie bialgebra structures of \(W\)-algebra \(W(2, 2)\) type ⋮ Lie Bialgebra Structures on the Lie Algebra ⋮ Lie bialgebras of generalized loop Virasoro algebras

Cites Work

• Unnamed Item
• Unnamed Item
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• On Lie and associative duals
• The algebraic structure of linearly recursive sequences under Hadamard product
• Physics for algebraists: Non-commutative and non-cocommutative Hopf algebras by a bicrossproduct construction
• The dual Poincaré-Birkhoff-Witt theorem
• The Hopf algebra of linearly recursive sequences
• Lie coalgebras
• A class of infinite-dimensional Lie bialgebras containing the Virasoro algebra
• An example of a non-zero Lie coalgebra M for which \(Loc(M)=0\)
• The structure of the dual Lie coalgebra of the Witt algebra

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