Deformation of modules of weighted densities on the superspace \({\mathbb{R}^{1|N}}\)
详细信息 查看全文
- 作者：M. Abdaoui (1)
H. Khalfoun (1)
I. Laraiedh (1) - 关键词：cohomology ; deformation ; weighted densities ; symbol ; 17B56 ; 53D55 ; 58H15
- 刊名：Acta Mathematica Hungarica
- 出版年：2015
- 出版时间：February 2015
- 年：2015
- 卷：145
- 期：1
- 页码：104-123
- 全文大小：372 KB
- 参考文献：1. Agrebaoui B., Ammar F., Lecomte P., Ovsienko V.: Multi-parameter deformations of the module of symbols of differential operators. Int. Math. Res. Not., 16, 847鈥?69 (2002) CrossRef
2. B. Agrebaoui, N. Ben Fraj, M. Ben Ammar and V. Ovsienko, Deformations of modules of differential forms, / J. Nonlinear Math. Phys., 10 (2003), 148鈥?56.
3. F. Ammar and K. Kammoun, Deformation of the Lie superalgebra \({\mathcal{K}}\) (1)-modules of symbols, / J. Gen. Lie Theory Appl., 3 (2009), 95鈥?11, arXiv:math.ph/0807.4811.
4. I. Basdouri and M. Ben Ammar, Deformation of \({\mathfrak{sl}(2)}\) and \({\mathfrak{osp}(1|2)}\) -modules of symbols, / Acta Math. Hungar., 137 (2012), 214鈥?23, arXiv:math.RT/1004.1700.
5. I. Basdouri, M. Ben Ammar, B. Dali and S. Omri, Deformation of \({{\rm Vect}_P}\) \({\mathbb{(R)}}\) -modules of symbols, arXiv:math.RT/0702664.
6. M. Ben Ammar and M. Boujelbene, sl(2)-Trivial deformations of \({{\rm Vect}_P}\) \({\mathbb{(R)}}\) -modules of symbols, / SIGMA, 4 (2008), 065.
7. M. Ben Ammar, N. Ben Fraj and S. Omri, The binary invariant differential operators on weighted densities on the superspace \({\mathbb{R}^{1|n}}\) and cohomology, / J. Math. Phys., 51 (2010), 043504.
8. N. Ben Fraj, A. Jabeur and I. Safi, The binary invariant differential operators on weighted densities on the superspace \({\mathbb{R}^{1|n}}\) and cohomology, / J. Lie Theory., 23 (2013), 575鈥?87.
9. C. H. Conley, Conformal symbols and the action of contact vector fields over the superline, arXiv:0712.1780v2 [math.RT].
10. A. Fialowski, Deformations of Lie algebras, / Mat. Sbornik USSR, 127 (169) (1985), 476鈥?82; English translation: / Math. USSR-Sb., 55 (1986), 467鈥?73.
11. A. Fialowski, An example of formal deformations of Lie algebras, in: / NATO Conference on Deformation Theory of Algebras and Applications (Il Ciocco, Italy, 1986), Kluwer (Dordrecht, 1988), pp. 375鈥?01.
12. A. Fialowski and D. B. Fuchs, Construction of miniversal deformations of Lie algebras, / J. Funct. Anal., 161 (1999), 76鈥?10.
13. D. B. Fuchs, / Cohomology of Infinite-dimensional Lie Algebras, Plenum Publ. (New York, 1986).
14. H. Gargoubi, N. Mellouli and V. Ovsienko, Differential operators on supercircle: conformally equivariant quantization and symbol calculus, / Lett. Math. Phys., 79 (2007), 51鈥?5.
15. P. Grozman, D. Leites and I. Shchepochkina, Lie subalgebras of string theories, / Acta Math. Vietnam., 26 (2001), 27鈥?3.
16. P. B. A. Lecomte, On the cohomology of \({\mathfrak{sl}(n + 1); \mathbb{R}}\) ) acting on differential operators and \({\mathfrak{sl}(n + 1); \mathbb{R}}\) )-equivariant symbols, / Indag. Math. Phys. NS., 11 (2000), 95鈥?114.
17. A. Nijenhuis and R. W. Richardson, Jr., Deformations of homomorphisms of Lie groups and Lie algebras, / Bull. Amer. Math. Soc., 73 (1967), 175鈥?79.
18. V. Ovsienko and C. Roger, 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 (1999), 211鈥?27.
19. R. W. Richardson, Deformations of subalgebras of Lie algebras, / J. Diff. Geom., 3 (1969), 289鈥?08. - 作者单位：M. Abdaoui (1)
H. Khalfoun (1)
I. Laraiedh (1)
1. D茅partement de Math茅matiques, Facult茅 des Sciences de Sfax, BP 802, 3038, Sfax, Tunisie - 刊物类别：Mathematics and Statistics
- 刊物主题：Mathematics
Sciences
Mathematics - 出版者：Akad茅miai Kiad贸, co-published with Springer Science+Business Media B.V., Formerly Kluwer Academic
- ISSN：1588-2632
文摘
Over the (1,N)-dimensional real superspace, \({N \geqq 3}\) , we study non-trivial deformations of the natural action of the orthosymplectic Lie superalgebra \({\mathfrak{osp}(N|2)}\) on the direct sum of the superspaces of weighted densities. We compute the necessary and sufficient integrability conditions of a given infinitesimal deformation of this action and prove that any formal deformation is equivalent to its infinitisemal part. Likewise we study the same problem for the Lie superalgebra \({\mathcal{K}(N)}\) of contact vector fields instead of \({\mathfrak{osp}(N|2)}\) getting the same results. This work is the simplest generalization of a result by I. Basdouri and M. Ben Ammar [4] and F. Ammar and K. Kammoun [3].