Cohomology of 𝔞𝔣𝔣(m|1) acting on the space of superpseudodifferential operators on the supercircle S1|m

DOI10.1142/S1793557118500572zbMath1396.53117OpenAlexW2625181920MaRDI QIDQ4578322

Nizar Ben Fraj, Meher Abdaoui, Hafedh Khalfoun

Publication date: 8 August 2018

Published in: Asian-European Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s1793557118500572

zbMATH Keywords

cohomologyPoisson superalgebraassinfe Lie superalgebrasuperspeudodifferential operator

Mathematics Subject Classification ID

Representations of Lie algebras and Lie superalgebras, algebraic theory (weights) (17B10) Virasoro and related algebras (17B68) Differentials and other special sheaves; D-modules; Bernstein-Sato ideals and polynomials (14F10) Deformation quantization, star products (53D55)

Cites Work

• 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
• On a trace functional for formal pseudo-differential operators and the symplectic structure of the Korteweg-deVries type equations
• Construction of miniversal deformations of Lie algebras
• Deforming the Lie algebra of vector fields on \(S^1\) inside the Poisson algebra on \(\dot T^*S^1\)
• Deformations of subalgebras of Lie algebras
• Differential groups and formal Lie theory for an infinite number of parameters
• On the Cohomology of the Lie Superalgebra of Contact Vector Fields on S1|2
• Deformations of Modules of Differential Forms
• Deformations of homomorphisms of Lie groups and Lie algebras
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