Homology of the Lie algebra of vector fields on the line

DOI10.1007/BF01086182zbMath0487.57011WikidataQ115394176 ScholiaQ115394176MaRDI QIDQ1165499

Boris L. Feigin, Dmitry Fuchs

Publication date: 1981

Published in: Functional Analysis and its Applications (Search for Journal in Brave)

zbMATH Keywords

Gelfand-Fuks cohomology of the Lie algebra of polynomial vector fields on the line with non-trivial coefficientshomology of the Lie algebra of vector fields on the line

Mathematics Subject Classification ID

Lie algebras of vector fields and related (super) algebras (17B66) Cohomology of classifying spaces for pseudogroup structures (Spencer, Gelfand-Fuks, etc.) (58H10) Cohomology of Lie (super)algebras (17B56) Classifying spaces for foliations; Gelfand-Fuks cohomology (57R32)

Related Items (32)

Singular projective bases and the affine Bol operator ⋮ Annihilators of tensor density modules ⋮ Cohomology of the Lie Superalgebra of Contact Vector Fields on 𝕂^1|1 and Deformations of the Superspace of Symbols ⋮ First space cohomology of the orthosymplectic Lie superalgebra \(\mathfrak {osp}(3|2)\) in the Lie superalgebra of superpseudodifferential operators ⋮ Classification of irreducible representations of Lie algebra of vector fields on a torus ⋮ Deformation of \(\mathfrak{sl}(2)\) and \(\mathfrak{osp}(1| 2)\)-modules of symbols ⋮ Length two extensions of modules for the Witt algebra ⋮ Deformations of nilpotent parts of the Neveu–Schwarz and Ramond superalgebras ⋮ Second cohomology of the Lie superalgebra of contact vector fields on weighted densities on the superspace \(\mathbb{K}^{1|n}\) ⋮ Cohomology of \(\mathrm{V ect}(\mathbb{R})\) acting on the space of bilinear differential operators ⋮ The binary \(\mathfrak{a} \mathfrak{f} \mathfrak{f}(n | 1)\)-invariant differential operators on weighted densities on the superspace \(\mathbb{R}^{1 | n}\) and \(\mathfrak{a} \mathfrak{f} \mathfrak{f}(n | 1)\)-relative cohomology ⋮ Bounded weight modules of the Lie algebra of vector fields on ℂ2 ⋮ Cohomology of 𝔞𝔣𝔣(1|1) acting on the space of n-ary linear differential operators on S1|1 ⋮ New realizations of deformed double current algebras and Deligne categories ⋮ Symmetries of Modules of Differential Operators ⋮ Cohomology and deformation of 𝔞𝔣𝔣(1|1) acting on differential operators ⋮ Classification of the indecomposable bounded admissible modules over the Virasoro Lie algebra with weightspaces of dimension not exceeding two ⋮ Deformation of \(\mathfrak{vect}(1)\)-modules of symbols ⋮ On sl(2)-relative cohomology of the Lie algebra of vector fields and differential operators ⋮ Deformations of some infinite-dimensional Lie algebras ⋮ The absolute rigidity of the Neveu–Schwarz and Ramond superalgebras ⋮ Cohomology of \(\mathfrak{sl}(2)\) acting on the space of \(n\)-ary differential operators on \(\mathbb{R} \) ⋮ Conformal symbols and the action of contact vector fields over the superline ⋮ Cohomology of \({\mathcal {K}(2)}\) acting on linear differential operators on the superspace \({\mathbb{R}^{1|2}}\) ⋮ On the Cohomology of the Lie Superalgebra of Contact Vector Fields onS^1|m ⋮ The binary invariant differential operators on weighted densities on the superspace R1∣n and cohomology ⋮ Bounded subquotients of pseudodifferential operator modules ⋮ Simple weight modules with finite weight multiplicities over the Lie algebra of polynomial vector fields ⋮ On the complex analytic Gel'fand-Fuks cohomology of open Riemann surfaces ⋮ First cohomology space of the orthosymplectic Lie superalgebra \(\mathfrak{osp}(n|2)\) in the Lie superalgebra of superpseudodifferential operators ⋮ Deforming 𝔥-trivial the Lie algebra Vect(S¹) inside the Lie algebra of pseudodifferential operators Ψ𝒟𝒪 ⋮ Equivalence classes of subquotients of supersymmetric pseudodifferential operator modules

Cites Work

• Unnamed Item
• The cohomology of the vector fields on a manifold
• Cohomology of Lie algebras of formal vector fields on the line

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