Hostname: page-component-848d4c4894-5nwft Total loading time: 0 Render date: 2024-06-01T19:00:52.412Z Has data issue: false hasContentIssue false

Jet Modules

Published online by Cambridge University Press:  20 November 2018

Yuly Billig*
Affiliation:
School of Mathematics and Statistics, Carleton University, Ottawa, ON, K1S 5B6 email: billig@math.carleton.ca
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

Type
Research Article
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, 188231.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, 2342.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, 33223333.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, 239264.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, 235251.Google Scholar
[L] Larsson, T. A., Lowest-energy representations of non-centrally extended diffeomorphism algebras. Comm. Math. Phys. 201(1999), no. 2, 461470.Google Scholar
[M] Mathieu, O., Classification of Harish-Chandra modules over the Virasoro algebra. Invent. Math. 107(1992), no. 2, 225234.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), 836866.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