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The second cohomology spaces of 𝒦(1) with coefficients in the superspace of weighted densities and deformations of the superspace of symbols on S 1|1

  • Boujemaâ Agrebaoui , Imed Basdouri ORCID logo EMAIL logo and Maha Boujelben
Published/Copyright: March 29, 2023
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Abstract

We explicitly describe the second cohomology of the Lie superalgebra 𝒦 ( 1 ) of contact vector fields on the supercircle S 1 | 1 with coefficients in the spaces of weighted densities. We deduce the second cohomology of 𝒦 ( 1 ) with coefficients in the Poisson algebra of pseudodifferential symbols on S 1 | 1 . We study formal deformations of the standard embedding of 𝒦 ( 1 ) into the Poisson superalgebra of pseudodifferential symbols.

MSC 2010: 53D55

Acknowledgements

We would like to thank Professor Mabrouk Ben Ammar and the referee for helpful suggestions and remarks.

References

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Received: 2022-05-22
Revised: 2022-10-09
Accepted: 2022-10-13
Published Online: 2023-03-29
Published in Print: 2023-06-01

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