The second cohomology spaces of 𝒦(1) with coefficients in the superspace of weighted densities and deformations of the superspace of symbols on <i>S</i> <sup>1|1</sup>-Reference-Cited by-同舟云学术

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

Published:2023-03-29 Issue:3 Volume:30 Page:321-327
ISSN:1072-947X
Container-title:Georgian Mathematical Journal
language:en
Short-container-title:

Author:

Agrebaoui Boujemaâ¹,Basdouri Imed²^ORCID,Boujelben Maha²

Affiliation:

1. Département de Mathématiques , Faculté des Sciences , Université de Sfax , Sfax , Tunisia

2. Département de Mathématiques , Faculté des Sciences , Université de Gafsa , Gafsa , Tunisia

Abstract

Abstract We explicitly describe the second cohomology of the Lie superalgebra 𝒦 ⁢ ( 1 )

{\mathcal{K}(1)}

of contact vector fields on the supercircle S 1 | 1

{S^{1|1}}

with coefficients in the spaces of weighted densities. We deduce the second cohomology of 𝒦 ⁢ ( 1 )

{\mathcal{K}(1)}

with coefficients in the Poisson algebra of pseudodifferential symbols on S 1 | 1

{S^{1|1}}

. We study formal deformations of the standard embedding of 𝒦 ⁢ ( 1 )

{\mathcal{K}(1)}

into the Poisson superalgebra of pseudodifferential symbols.

Publisher

Walter de Gruyter GmbH

Subject

General Mathematics

Link

https://www.degruyter.com/document/doi/10.1515/gmj-2023-2014/pdf

Reference14 articles.

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2. B. Agrebaoui and N. Ben Fraj, On the cohomology of the Lie superalgebra of contact vector fields on S 1 / 1 {S^{1/1}} , Bull. Soc. Roy. Sci. Liège 72 (2003), no. 6, 365–375.

3. I. Basdouri, M. Ben Ammar, N. Ben Fraj, M. Boujelbene and K. Kammoun, Cohomology of the Lie superalgebra of contact vector fields on 𝕂 1 | 1 {\mathbb{K}^{1|1}} and deformations of the superspace of symbols, J. Nonlinear Math. Phys. 16 (2009), no. 4, 373–409.

4. O. Basdouri, Deformation of 𝔞 ⁢ 𝔣 ⁢ 𝔣 ⁢ ( 1 ) {\mathfrak{aff}(1)} -modules of pseudo-differential operators and symbols, J. Pseudo-Differ. Oper. Appl. 7 (2016), no. 2, 157–179.

5. O. Basdouri, A. Braghtha and S. Hammami, The second cohomology spaces 𝒦 ⁢ ( 2 ) {\mathcal{K}(2)} with coefficients in the superspace of weighted densities, Ukrainian Math. J. 72 (2021), no. 10, 1522–1535.

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