\({\mathfrak {osp}}(2|2)\) -Trivial deformations of modules of weighted densities on the superspace 详细信息    查看全文

• 作者：Salem Omri
• 关键词：Cohomology ; Deformation ; Lie superalgebra ; Orthosymplectic Lie superalgebra ; 17B56 ; 53D55 ; 14F40 ; 14F43 ; 13D10
• 刊名：Journal of Pseudo-Differential Operators and Applications
• 出版年：2015
• 出版时间：December 2015
• 年：2015
• 卷：6
• 期：4
• 页码：461-485
• 全文大小：571 KB
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  2.Agrebaoui, B., Ben Fraj, N., Ben Ammar, M., Ovsienko, V.: Deformations of modules of differential forms. J. Nonlinear Math. Phys. 10, 148鈥?56 (2003)
  3.Basdouri, I., Ben Ammar, M., Ben Fraj, N., Boujelbene, M., Kammoun, K.: Cohomology of the Lie superalgebra of contact vector fields on \({\mathbb{K}}^{1|1} \) and deformations of the superspace of symbols. J. Nonlinear Math. Phys. 16, 373 (2009)MATH MathSciNet CrossRef
  4.Basdouri, I., Ben Ammar, M., Dali, B., Omri, S.: Deformation of \({\text{ Vect }_{\rm P}}({\mathbb{R}})\) -modules of symbols. arXiv:鈥媘ath.鈥婻T/鈥?702664
  5.Ben Ammar, M., Boujelbene, M.: sl(2)-Trivial deformations of \({\text{ Vect }_{\rm P}}({\mathbb{R}})\) -modules of symbols. SIGMA 4, 065 (2008)MathSciNet
  6.Ben Fraj, N.: Cohomology of \({\cal K}(2)\) . Lett. Math. Phys. 86, 159鈥?75 (2008)
  7.Ben Fraj, N., Laraiedh, I., Omri, S.: Supertransvectants, cohomology and deformations. J. Math. Phys. 54, 023501 (2013)MathSciNet CrossRef
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  10.Fuchs, D.B.: Cohomology of Infinite-Dimensional Lie Algebras. Plenum Publ, New York (1986)
  11.Gargoubi, H., Mellouli, N., Ovsienko, V.: Differential operators on supercircle: conformally equivariant quantization and symbol calculus. Lett. Math. Phys. 79, 51鈥?5 (2007)MATH MathSciNet CrossRef
  12.Gargoubi, H., Ovsienko, V.: Supertransvectants and symplectic geometry. arXiv:鈥?0705.鈥?411v1 [math-ph]
  13.Gieres, F., Theisen, S.: Superconformally covariant operators and super W-algebras. J. Math. Phys. 34, 5964鈥?985 (1993)MATH MathSciNet CrossRef
  14.Gordan, P.: Invariantentheorie. Teubner, Leipzig (1887)MATH
  15.Nijenhuis, A., Richardson Jr, R.W.: Deformations of homomorphisms of Lie groups and Lie algebras. Bull. Am. Math. Soc. 73, 175鈥?79 (1967)MATH MathSciNet CrossRef
  16.Ovsienko, V., Roger, C.: Deforming the Lie algebra of vector fields on \(S^1\) inside the Lie algebra of pseudodifferential operators on \(S^1\) . AMS Transl. Ser. 2 (Adv. Math. Sci.) 194, 211鈥?27 (1999)MathSciNet
  17.Ovsienko, V., Roger, C.: Deforming the Lie algebra of vector fields on \(S^1\) inside the Poisson algebra on \(\dot{T}^*S^1\) . Commun. Math. Phys. 198, 97鈥?10 (1998)MATH MathSciNet CrossRef
  18.Richardson, R.W.: Deformations of subalgebras of Lie algebras. J. Differ. Geom. 3, 289鈥?08 (1969)MATH
  
• 作者单位：Salem Omri (1)
  
  1. D茅partement de Math茅matiques, Facult茅 des Sciences de Gafsa, Zarroug, 2112, Gafsa, Tunisia
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：None Assigned
• 出版者：Birkh盲user Basel
• ISSN：1662-999X

文摘

We consider the action of the Lie superalgebra \({\mathcal {K}}(2)\) by Lie derivative on the superspace of linear differential operators acting on the direct sum of the superspaces of weighted densities \({\mathfrak {S}}^{n}_{\beta }=\bigoplus _{k=0}^{2n}{\mathfrak {F}}^2_{\beta -\frac{k}{2}}\). We study the generic formal deformations of this action that become trivial once restricted to the orthosymplectic Lie superalgebra \({\mathfrak {osp}}(2|2)\). Necessary and sufficient conditions for integrability of any infinitesimal deformations of \({\mathfrak {S}}^{n}_{\beta }\) are given. We describe completely the formal deformations for some spaces \({\mathfrak {S}}^{n}_{\beta }\) and we give concrete examples of non trivial deformations. Keywords Cohomology Deformation Lie superalgebra Orthosymplectic Lie superalgebra