Cohomology and deformation of 𝔞𝔣𝔣(1|1) acting on differential operators

DOI10.1142/S021988781850072XzbMath1390.17028OpenAlexW2780045383WikidataQ115245345 ScholiaQ115245345MaRDI QIDQ4635335

Salem Omri, Khaled Basdouri

Publication date: 16 April 2018

Published in: International Journal of Geometric Methods in Modern Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s021988781850072x

zbMATH Keywords

cohomologydeformationdifferential operatorsaffine Lie superalgebraNeveu-Schwarz

Mathematics Subject Classification ID

Pseudodifferential operators as generalizations of partial differential operators (35S05) Geometry and quantization, symplectic methods (81S10) Deformations of general structures on manifolds (58H15) Deformation quantization, star products (53D55) Cohomology of Lie (super)algebras (17B56) Functional analysis on superspaces (supermanifolds) or graded spaces (46S60)

Cites Work

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• Deformation of \(\mathfrak{aff}(1)\)-modules of pseudo-differential operators and symbols
• \(\mathfrak{sl}(2)\)-trivial deformations of \(\text{Vect}_{\text{Pol}}(\mathbb R)\)-modules of symbols
• Homology of the Lie algebra of vector fields on the line
• Construction of miniversal deformations of Lie algebras
• Deforming the Lie algebra of vector fields on \(S^1\) inside the Poisson algebra on \(\dot T^*S^1\)
• 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
• Deformation of \(\mathfrak{vect}(1)\)-modules of symbols
• 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 Modules of Differential Forms
• Cohomology of the Lie Superalgebra of Contact Vector Fields on 𝕂^1|1 and Deformations of the Superspace of Symbols
• Deformations of homomorphisms of Lie groups and Lie algebras
• First cohomology of 𝔞𝔣𝔣(1) and 𝔞𝔣𝔣(1|1) acting on linear differential operators

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