Abstract
Vertex representations are obtained for toroidal Lie algebras for any number of variables. These representations afford representations of certainn-variable generalizations of the Virasoro algebra that are abelian extensions of the Lie algebra of vector fields on a torus.
Similar content being viewed by others
References
[B] Borcherds, R.: Vertex algebras, Kac-Moody algebras and the Monster. Proc. Natl. Acad. Sci. USA83, 3068–3071 (1986)
[BM] Bermans, S., Moody, R.V.: Lie algebras graded by finite root systems and the intersection matrix algebras of Slodowy. Invent. Math.108, 323–347 (1992)
[BC] Berman, S., Cox, B.: Enveloping algebras and representations of toroidal Lie algebras. Pacific J. Math., to appear
[EMY] Eswara Rao, S., Moody, R.V., Yokonuma, T.: Lie algebras and Weyl groups arising from vertex operator representations. Nova J. of Algebra and Geometry1, 15–58 (1992)
[FM] Fabbri, M., Moody, R.V.: Irreducible representations of Virasoro-toroidal Lie algebras. Commun. Math. Phys., to appear
[G] Garland, H.: The arithemetic theory of loop groups. Math. IHES52, 5–136 (1980)
[GO] Goddard, P., Olive, D.: Algebras, lattices and strings, Vertex operators in Mathematics and Physics. Publ. Math. Sci. Res. Inst. #3, Springer-Verlag, 1984
[K] Kassel, C.: Kahler differentials and coverings of complex simple Lie algebras extended over a commutative algebra. J. Pure and Appl. Algebra34, 256–275 (1985)
[KF] Frenkel, I., Kac, V.: Basic representation of affine Lie algebras and dual resonance models. Invent. Math.62, 23–66 (1980)
[KMPS] Kass, S., Moody, R.V., Patera, J., Slansky, R.: Representations of Affine Algebras and Branching Rules. Berkeley: University of California Press 1990
[MEY] Moody, R.V., Eswara Rao, S., Yokonuma, T.: Toroidal Lie algebras and vertex representations. Geom. Ded.35, 283–307 (1990)
[MS] Moody, R.V., Shi, Z.: Toroidal Weyl groups. Nova J. Algebra and Geometry1, 317–337 (1992)
Author information
Authors and Affiliations
Additional information
Communicated by A. Jaffe
Work supported in part by the Natural Sciences and Engineering Research Council of Canada.
Rights and permissions
About this article
Cite this article
Eswara Rao, S., Moody, R.V. Vertex representations forN-toroidal Lie algebras and a generalization of the Virasoro algebra. Commun.Math. Phys. 159, 239–264 (1994). https://doi.org/10.1007/BF02102638
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02102638