Hostname: page-component-cd9895bd7-gvvz8 Total loading time: 0 Render date: 2024-12-18T22:47:50.460Z Has data issue: false hasContentIssue false
  • English
  • Français

Jet Modules

Published online by Cambridge University Press:  20 November 2018

Yuly Billig
Yuly Billig*
Affiliation:
School of Mathematics and Statistics, Carleton University, Ottawa, ON, K1S 5B6 email: [email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In this paper we classify indecomposable modules for the Lie algebra of vector fields on a torus that admit a compatible action of the algebra of functions. An important family of such modules is given by spaces of jets of tensor fields.

Keywords

17B6658A20
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 59 , Issue 4 , 01 August 2007 , pp. 712 - 729
Copyright
Copyright © Canadian Mathematical Society 2007

References

[BB] Berman, S. and Billig, Y., Irreducible representations for toroidal Lie algebras. J. Algebra 221(1999), no. 1, 188–231.Google Scholar
[B] Billig, Y., Energy-momentum tensor for the toroidal Lie algebras. ArXiv:math.RT/0201313.Google Scholar
[B2] Billig, Y., A category of modules for the full toroidal Lie algebra. Int. Math. Res. Not. 2006, Art. ID 68935.Google Scholar
[BZ] Billig, Y. and Zhao, K., Weight modules over exp-polynomial Lie algebras. J. Pure Appl. Algebra 191(2004), no. 1-2, 23–42.Google Scholar
[ER] Eswara Rao, S., Partial classification of modules for Lie algebra of diffeomorphisms of d-dimensional torus. J. Math. Phys. 45(2004), no. 8, 3322–3333.Google Scholar
[EM] Eswara Rao, S. and R.Moody, V., Vertex representations for n-toroidal Lie algebras and a generalization of the Virasoro algebra. Comm. Math. Phys. 159(1994), no. 2, 239–264.Google Scholar
[GO] Gargoubi, H. and Ovsienko, V. Yu., Space of linear differential operators on the real line as a module over the Lie algebra of vector fields. Internat. Math. Res. Notices 1996, no. 5, 235–251.Google Scholar
[L] Larsson, T. A., Lowest-energy representations of non-centrally extended diffeomorphism algebras. Comm. Math. Phys. 201(1999), no. 2, 461–470.Google Scholar
[M] Mathieu, O., Classification of Harish-Chandra modules over the Virasoro algebra. Invent. Math. 107(1992), no. 2, 225–234.Google Scholar
[O] Olver, P. J., Applications of Lie groups to differential equations. Graduate Texts in Mathematics 107, Springer-Verlag, New York, 1986.Google Scholar
[Ru] Rudakov, A. N., Irreducible representations of infinite-dimensional Lie algebras of Cartan type. Math. USSR Izv. 8(1974), 836–866.Google Scholar
[S] Saunders, D. J., The geometry of jet bundles. London Mathematical Society Lecture Note Series 142, Cambridge University Press, Cambridge, 1989.Google Scholar
[vdW] van der Waerden, B. L., Modern Algebra. Frederick Ungar Publ., New York, 1949.Google Scholar