Low-Dimensional Cohomology Groups of the Lie Algebras W(a,b)

DOI10.1080/00927871003591835zbMath1272.17024OpenAlexW2002145110MaRDI QIDQ3084549

Yufeng Pei, Shoulan Gao, Cuipo (Cuibo) Jiang

Publication date: 25 March 2011

Published in: Communications in Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/00927871003591835

zbMATH Keywords

Witt algebraderivation algebracentral extension

Mathematics Subject Classification ID

Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras (17B67) Virasoro and related algebras (17B68) Cohomology of Lie (super)algebras (17B56)

Related Items (27)

Structures of a class of deformative super W-algebras ⋮ Classification of simple Harish-Chandra modules for map (super)algebras related to the Virasoro algebra ⋮ A category of restricted modules for the Ovisenko-Roger algebra ⋮ Structure of the planar Galilean conformal algebra ⋮ Structures of generalized loop planar Galilean conformal algebras ⋮ Symmetries at null boundaries: two and three dimensional gravity cases ⋮ Biderivations of the twisted Heisenberg–Virasoro algebra and their applications ⋮ Some modules over Lie algebras related to the Virasoro algebra ⋮ Derivations and Automorphism Group of Original Deformative Schrödinger-Virasoro Algebra ⋮ Super-biderivations and post-Lie superalgebras on some Lie superalgebras ⋮ On rigidity of 3d asymptotic symmetry algebras ⋮ Classification of Harish-Chandra modules over some Lie algebras related to the Virasoro algebra ⋮ Local derivations on the Lie algebra W (2, 2) ⋮ Derivations, extensions, and rigidity of subalgebras of the Witt algebra ⋮ Deformations on the twisted Heisenberg-Virasoro algebra ⋮ Unnamed Item ⋮ Biderivations and commutative post-Lie algebra structures on the Lie algebra \(\mathcal{W}(a,b)\) ⋮ Modules over the algebra \(\mathcal{V}ir(a,b)\) ⋮ Representations of the ExtendedW-Algebra ⋮ The Frobenius-Virasoro algebra and Euler equations. II: Multi-component cases ⋮ Lie bialgebra structures on the twisted Heisenberg-Virasoro algebra ⋮ Tensor product weight modules of Schrödinger-Virasoro algebras ⋮ On stabilization of Maxwell-BMS algebra ⋮ The deformed Lie algebra of differential operators of order at most one ⋮ Realizations of conformal current-type Lie algebras ⋮ Boundary Heisenberg algebras and their deformations ⋮ Derivations of the nongraded Witt algebra with coefficients in tensor modules

Cites Work

• \(W\)-algebra \(W\)(2, 2) and the vertex operator algebra \({L(\frac{1}{2},\,0)\,\otimes\, L(\frac{1}{2},\,0)}\)
• The higher rank Virasoro algebras
• On a problem of V. G. Kac: the classification of certain simple graded Lie algebras
• Cohomology groups of infinite dimensional algebras
• Moduli spaces of curves and representation theory
• Derivations and central extensions of finitely generated graded Lie algebras
• Universal enveloping algebras of Leibniz algebras and (co)homology
• On Leibniz homology
• Extensions of the Virasoro group and the Virasoro algebra by modules of tensor densities on \(S^ 1\)
• SECOND COHOMOLOGY GROUP OF GENERALIZED WITT TYPE LIE ALGEBRAS AND CERTAIN REPRESENTATIONS
• Leibniz Central Extensions on Some Infinite-Dimensional Lie Algebras
• Structure of the Extended Schrödinger–Virasoro Lie Algebra $\widetilde{\mathfrak{sv}}$
• Derivations, isomorphisms, and second cohomology of generalized Witt algebras
• Representations of the Twisted Heisenberg–Virasoro Algebra at Level Zero
• The Second Leibniz Homology Group for Kac-Moody Lie Algebras
• A cohomological characterization of Leibniz central extensions of Lie algebras
• The Derivation Algebra and Automorphism Group of the Twisted Heisenberg–Virasoro Algebra
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