Geodesic
The Virasoro Algebra and Some Exceptional Lie and Finite Groups
Symmetry, integrability and geometry: methods and applications, Tome 3 (2007) Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We describe a number of relationships between properties of the vacuum Verma module of a Virasoro algebra and the automorphism group of certain vertex operator algebras. These groups include the Deligne exceptional series of simple Lie groups and some exceptional finite simple groups including the Monster and Baby Monster.
Keywords: vertex operator algebras; Virasoro algebras; Deligne exceptional series; Monster group. 
@article{SIGMA_2007_3_a7,
     author = {Michael P. Tuite},
     title = {The {Virasoro} {Algebra} and {Some} {Exceptional} {Lie} and {Finite} {Groups}},
     journal = {Symmetry, integrability and geometry: methods and applications},
     year = {2007},
     volume = {3},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SIGMA_2007_3_a7/}
}
TY  - JOUR
AU  - Michael P. Tuite
TI  - The Virasoro Algebra and Some Exceptional Lie and Finite Groups
JO  - Symmetry, integrability and geometry: methods and applications
PY  - 2007
VL  - 3
UR  - http://geodesic.mathdoc.fr/item/SIGMA_2007_3_a7/
LA  - en
ID  - SIGMA_2007_3_a7
ER  - 
%0 Journal Article
%A Michael P. Tuite
%T The Virasoro Algebra and Some Exceptional Lie and Finite Groups
%J Symmetry, integrability and geometry: methods and applications
%D 2007
%V 3
%U http://geodesic.mathdoc.fr/item/SIGMA_2007_3_a7/
%G en
%F SIGMA_2007_3_a7
Michael P. Tuite. The Virasoro Algebra and Some Exceptional Lie and Finite Groups. Symmetry, integrability and geometry: methods and applications, Tome 3 (2007). http://geodesic.mathdoc.fr/item/SIGMA_2007_3_a7/

[1] Borcherds R., “Vertex algebras, Kac–Moody algebras and the Monster”, Proc. Natl. Acad. Sci. USA, 83 (1986), 3068–3071 | DOI | MR | Zbl

[2] Deligne P., “La série exceptionnelle de groupes de Lie (The exceptional series of Lie groups)”, C. R. Acad. Sci. Paris Sér. I Math., 322 (1996), 321–326 | MR | Zbl

[3] Dong C., Mason G., “Holomorphic vertex operator algebras of small central charge”, Pacific J. Math., 213 (2004), 253–266 ; math.QA/0203005 | DOI | MR | Zbl

[4] Frenkel I., Huang Y-Z., Lepowsky J., On axiomatic approaches to vertex operator algebras and modules, Mem. Amer. Math. Soc., no. 494, 1993, 64 pp. | MR

[5] Frenkel I., Lepowsky J., Meurman A., Vertex operator algebras and the Monster, Academic Press, New York, 1988 | MR

[6] Griess R. L., “The vertex operator algebra related to $E_8$ with automorphism group $O^+(10,2)$”, The Monster and Lie algebras (1996, Columbus, Ohio State University), Math. Res. Inst. Public., 7, de Gruyter, Berlin, 1998 | MR | Zbl

[7] Hoehn G., “Selbstduale Vertexoperatorsuperalgebren und das Babymonster”, Dissertation, Rheinische Friedrich-Wilhelms-Universitat Bonn (Bonn, 1995), Bonn. Math. Sch., 286, Universität Bonn Mathematisches Institut, Bonn, 1996, 1–85 | MR

[8] Kac V., Vertex operator algebras for beginners, University Lecture Series, 10, AMS, Boston, 1998 | Zbl

[9] Kac V., Raina A. K., Bombay lectures on highest weight representations of infinite dimensional Lie algebras, World Scientific, Singapore, 1987 | MR

[10] Li H., “Symmetric invariant bilinear forms on vertex operator algebras”, J. Pure Appl. Algebra, 96 (1994), 279–297 | DOI | MR | Zbl

[11] Matsuo A., “Norton's trace formula for the Griess algebra of a vertex operator algebra with large symmetry”, Comm. Math. Phys., 224 (2001), 565–591 ; math.QA/0007169 | DOI | MR

[12] Maruoka H., Matsuo A., Shimakura H., Trace form ulas for representations of simple Lie algebras via vertex operator algebras, unpublished preprint, 2005 | MR

[13] Matsuo A., Nagatomo K., Axioms for a vertex algebra and the locality of quantum fields, MSJ Memoirs, 4, Mathematical Society of Japan, Tokyo, 1999 ; hep-th/9706118 | MR

[14] Schellekens A. N., “Meromorphic $C=24$ conformal field theories”, Comm. Math. Phys., 153 (1993), 159–185 ; hep-th/9205072 | DOI | MR | Zbl

[15] Tuite M. P. (to appear)