Cohomology of the Lie Superalgebra of Contact Vector Fields on 𝕂1|1 and Deformations of the Superspace of Symbols

DOI10.1142/S1402925109000431zbMath1238.17015arXivmath/0702645OpenAlexW2119910397MaRDI QIDQ5306083

Maha Boujelbene, K. Kamoun, Mabrouk Ben Ammar, Imed Basdouri, Nizar Ben Fraj

Publication date: 29 March 2010

Published in: Journal of Nonlinear Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0702645

zbMATH Keywords

cohomology of Lie superalgebrasLie superalgebras of vector fields

Mathematics Subject Classification ID

Lie algebras of vector fields and related (super) algebras (17B66) Cohomology of Lie (super)algebras (17B56)

Related Items

\(\mathfrak{osp}(2|2)\)-trivial deformations of modules of weighted densities on the superspace \(\mathbb R^{1|2}\) ⋮ Cohomology of 𝔞𝔣𝔣(2|1) acting on the space of linear differential operators on the superspace ℝ1|2 ⋮ First space cohomology of the orthosymplectic Lie superalgebra \(\mathfrak {osp}(3|2)\) in the Lie superalgebra of superpseudodifferential operators ⋮ Deformation of \(\mathfrak{aff}(1)\)-modules of pseudo-differential operators and symbols ⋮ Deformation of \(\mathfrak{sl}(2)\) and \(\mathfrak{osp}(1| 2)\)-modules of symbols ⋮ Second cohomology of the Lie superalgebra of contact vector fields on weighted densities on the superspace \(\mathbb{K}^{1|n}\) ⋮ 1-cocycles on the group of contactomorphisms on the supercircles \(S^{1|1}\) and \(S^{1|2}\) generalizing the Schwarzian derivative ⋮ Cohomology of \(\mathfrak {osp}(2|2)\) acting on spaces of linear differential operators on the superspace \(\mathbb{R}^{1|2}\) ⋮ 1-Cocycles on the group of contactomorphisms on the supercircle S 1|3 generalizing the Schwarzian derivative ⋮ 𝔰𝔩(2, ℝ)-invariant 3-ary differential operators and cohomology of 𝔰𝔩(2, ℝ) acting on 3-ary differential operators ⋮ Cohomology of orthosymplectic Lie superalgebra acting on λ-densities on ℝ1|n ⋮ The second cohomology spaces of \(\mathcal{K} (1)\) with coefficients in the superspace of weighted densities and deformations of the superspace of symbols on \(S^{1|1} \) ⋮ On 𝔬𝔰𝔭(1|2)-relative cohomology of the Lie superalgebra of contact vector fields on ℝ1|1 ⋮ Cohomology of \({\mathfrak{osp}}(1|2)\) acting on linear differential operators on the supercircle \(S^{1|1}\) ⋮ Cohomology and deformation of 𝔞𝔣𝔣(1|1) acting on differential operators ⋮ Deformation of 𝔬𝔰𝔭(2|2)-modules of weighted densities on ℝ1|2 ⋮ Supertransvectants, cohomology, and deformations ⋮ On \(\mathfrak{osp}(2|2)\)-relative cohomology of the Lie superalgebra of contact vector fields and deformations ⋮ First cohomology of 𝔞𝔣𝔣(1) and 𝔞𝔣𝔣(1|1) acting on linear differential operators ⋮ Cohomology of \({\mathcal {K}(2)}\) acting on linear differential operators on the superspace \({\mathbb{R}^{1|2}}\) ⋮ The binary invariant differential operators on weighted densities on the superspace R1∣n and cohomology ⋮ Deforming 𝔥-trivial the Lie algebra Vect(S¹) inside the Lie algebra of pseudodifferential operators Ψ𝒟𝒪

Cites Work

• Differential operators on supercircle: conformally equivariant quantization and symbol calculus
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• Construction of miniversal deformations of Lie algebras
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• Cohomology of \({\mathfrak{osp}}(1|2)\) acting on linear differential operators on the supercircle \(S^{1|1}\)
• Deformations of subalgebras of Lie algebras
• DEFORMATIONS OF LIE ALGEBRAS
• Superconformally covariant operators and super-W-algebras
• Deformations of Modules of Differential Forms
• PROJECTIVE AND CONFORMAL SCHWARZIAN DERIVATIVES AND COHOMOLOGY OF LIE ALGEBRAS VECTOR FIELDS RELATED TO DIFFERENTIAL OPERATORS
• Deformations of homomorphisms of Lie groups and Lie algebras