Framed vertex operator algebras, codes and the moonshine module

Communications in Mathematical Physics

Volumn 193, Issue 2, 1998, Pages 407-448

  Dong, Chongying ^a   Griess Jr , Robert L ^b   Höhn, Gerald ^c  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b UNIVERSITY OF MICHIGAN   (United States)

^c UNIVERSITY OF FREIBURG   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0032478471     PISSN: 00103616     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002200050335     Document Type: Article

References (52)

1. Assmus, E.F. Jr., and Key, J.D.: Designs and Their Codes Cambridge: Cambridge Univ. Press, 1993
2. Conway, J.H., Curtis, R.T., Norton, S.P., Parker R.P. and Wilson. R.A.: Atlas of Finite Groups. Oxford: Clarendon Press, 1985
3. Bonnecaze, A. and Solé, P.: Quaternary constructions of formally self-dual binary codes and unimodular lattices. Algebraic coding (Paris, 1993), Lecture Notes in Comput. Sci., 781, Berlin: Springer, 1994, pp. 194-205
4. Borcherds, R.E.: Vertex algebras, Kac-Moody algebras, and the Monster. Proc. Natl. Acad. Sci. USA 83, 3068-3071 (1986)
5. Betten, A.: Personal communication
6. Conder, M. and McKay, J.: Markings of the Golay code. New Zealand J. Mathematics 25, 133-139 (1996)
7. Carter, R.: Simple Groups of Lie Type. Wiley Classics Library, London, New York, Sydney, Toronto: John Wiley and Sons, 1989
8. Conway, J.: A characterization of Leech's lattice. Invent. Math. 7, 137-142 (1969)
9. Conway, J. and Sloane, N.J.A.: Sphere packings. Lattices and Groups. Berlin-Heidelberg-New York: Springer, 1989
10. Conway, J. and Sloane, N.J.A.: Self-dual Codes over the Integers Modulo 4. J. of Combinatorial Th., Series A 62, 30-45 (1993)
11. Conway, J. and Sloane, N.J.A.: Lexicographic codes: error-correcting codes from game theory, Trans. on Information theory 32, 337-348 (1986)
12. Dolan, L., Goddard, P. and Montague, P.: Conformal field theory of twisted vertex operators. Nucl. Phys. B338, 529 (1990)
13. Dolan, L., Goddard, P. and Montague, P.: Conformai field theory, triality and the Monster group. Phys. Lett. B236, 165 (1990)
14. Dong, C.: Vertex algebras associated with even lattices. J. Algebra 160, 245-265 (1993)
15. Dong, C.: Twisted modules for vertex algebras associated with even lattices. J. Algebra 165, 90-112 (1994)
16. Dong, C.: Representations of the moonshine module vertex operator algebra. Contemporary Math. 175, 27-36 (1994)
17. Dong, C. and Lepowsky, J.: Generalized Vertex Algebras and Relative Vertex Operators. Progress in Math. Vol. 112, Boston: Birkhäuser, 1993
18. Dong, C. and Lepowsky, J.: The algebraic structure of relative twisted vertex operators. J. Pure and Applied Algebra 110, 259-295 (1996)
19. Dong, C., Li, H. and Mason, G.G.: Regularity of rational vertex operator algebras. Advances. in Math. 32, 148-166 (1997)
20. Dong, C., Li, H. and Mason, G.: Compact automorphism groups of vertex operator algebras. International Math. Research Notices 18, 913-921 (1996)
21. Dong, C., Li, H. and Mason, G.: Twisted representations of vertex operator algebras. Math. Ann. to appear, q-alg/9509005
22. Dong, C., Li, H. and Mason, G.: Modular invariance of trace functions in orbifold theory. q-alg/9703016
23. Dong, C. and Lin, Z.: Induced modules for vertex operator algebras. Commun. Math. Phys. 179, 157-184 (1996)
24. Dong, C. and Mason, G.: On quantum Galois theory. Duke Math. J. 86, 305-321 (1997)
25. Dong, C., Mason, G. and Zhu, Y.: Discrete series of the Virasoro algebra and the moonshine module. Proc. Symp. Pure. Math., American Math. Soc. 56 II, 295-316 (1994)
26. Frenkel, I.B., Lepowsky, J. and Meurman, A.: Vertex Operator Algebras and the Monster. Pure and Applied Math. Vol. 134, New York: Academic Press, 1988
27. Frenkel, I. and Zhu, Y.: Vertex operator algebras associated to representations of affine and Virasoro algebras, Duke Math. J. 66, 123-168 (1992)
28. Friedan, D., Qiu, Z. and Shenker, S.: Details of the non-unitarity proof for highest weight representations of Virasoro Algebra, Commun. Math. Phys. 107, 535-542 (1986)
29. Griess, R.L., Jr.: The Friendly Giant. Invent. Math. 69, 1-102 (1982)
30. Griess, R.L., Jr.: Twelve Sporadic Groups Book to be published by Springer-Verlag
31. Goddard, P., Kent, A. and Olive, D.: Unitary representations of the Virasoro Algebra and super-Virasoro algebras Commun. Math. Phys. 103, 105-119 (1986)
32. Höhn, G.: Selbstduale Vertexoperator-Superalgebren und das Babymonster, Ph.D. thesis, University of Bonn, 1995. See: Bonner mathematische Schriften 286, (1996)
33. Höhn, G.: Selbstduale Vertexoperator-Superalgebren und das Babymonster, Ph.D. thesis, University of Bonn, 1995. See: Bonner mathematische Schriften 286, (1996)
34. Höhn, G.: Self-dual codes over the Kleinian fourgroup. Preprint 1996
35. Höhn. G.: Simple current extensions of vertex operator algebras and the cohomology of K(π, 2). In preparation
36. Huang, Yi-Zhi: Intertwining Operator Algebras, genus-zero Modular Functors and genus-zero Conformal Field Theories. In: Operads, Proceedings of Renaissance Conferences. ed. J.-L. Loday, J. Stasheff, and A. A. Voronov, Contemporary Math., Vol. 202, Providence, RI: Amer. Math. Soc., 1997, pp. 335-355
37. Huang, Yi-Zhi: A Jacobi identity intertwiner algebras. q-alg/9704008
38. Kac, V. and Raina, A.: Bombay Lectures on Highest Weight Representations, Singapore: World Sci., 1987
39. Kac, V. and Wang, W.: Vertex operator superalgebras and representations. Contemporary Math. Vol. 175, 161-191 (1994)
40. Li, H.: Symmetric invariant bilinear forms on vertex operator algebras. J. Pure and Appl. Alg. 96, 279-297 (1994)
41. Li, H.: Representation theory and tensor product theory for vertex operator algebras. Ph.D. thesis, Rutgers University, 1994
42. Mac Williams, F.J. and Sloane, N.J.A.: The Theory of Error-Correcting Codes. Amsterdam: Elsevier Science Publishers B.V., 1977; The Theory of Error-Correcting Codes. Amsterdam: North Holland, second reprint 1983
43. Mac Williams, F.J. and Sloane, N.J.A.: The Theory of Error-Correcting Codes. Amsterdam: Elsevier Science Publishers B.V., 1977; The Theory of Error-Correcting Codes. Amsterdam: North Holland, second reprint 1983
44. Miyamoto, M.: Griess algebras and conformai vectors in vertex operator algebras. J. Algebra 179, 523-548 (1996)
45. Miyamoto, M.: Binary codes and vertex operator superalgebras. J. Algebra 181, 207-222 (1996)
46. Miyamoto, M.: Representation theory of Code VOA and construction of VOAs. Preprint (1996)
47. Moore, G. and Seiberg, N.: Classical and quantum conformal field theory. Commun. Math. Phys. 123, 177-254 (1989)
48. Mossberg, G.: Axiomatic vertex algebras and the Jacobi identity. J. Algebra, 956-1010 (1994)
49. Schellekens, A.N.: Meromorphic c = 24 Conformal Field Theories. Commun. Math. Phys. 153, 159 (1993)
50. Schönert, M. et al.: GAP: Groups, Algorithms and Programming. Lehrstuhl D für Mathematik, Aachen, 1994
51. Venkov, B.B.: The classification of integral even unimodular 24-dimensional quadratic forms. Trudy Matem. Inst. i. V. A. Steklova 148, 65-76 (1978)
52. Wang, W.: Rationality of Virasoro vertex operator algebras. Duke Math. J. IMRN 71, 197-211 (1993)