On abelian coset generalized vertex algebras

Communications in Contemporary Mathematics

Volumn 3, Issue 2, 2001, Pages 287-340

  Li, Haisheng ^a  

^a RUTGERS UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0007093020     PISSN: 02191997     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0219199701000366     Document Type: Article

References (61)

1. K. Bardakci and M. B. Halpern, New dual quark models, Phys. Rev. D3 (1971) 2493-2506.
2. J. Borcea, Dualities, affine vertex operator algebras, and geometry of complex polynomials, Ph.D. Dissertation, University of Lund, Sweden (1998).
3. R. E. Borcherds, Vertex algebras, Kac-Moody algebras, and the Monster, Proc. Natl. Acad. Sci. USA 83 (1986) 3068-3071.
4. d conformal field theories, hep-th/9710036.
5. d parafermions from constrained WZNW theories, hep-th/9712243.
6. A. V. Bratchikov, Generalized abelian coset conformal field theories, hep-th/9912112.
7. S. Capparelli, On some representations of twisted affine Lie algebras and combinatorial identities, J. Algebra 154 (1993) 335-355.
8. C. Dong, Vertex algebras associated with even lattices, J. Algebra 160 (1993) 245-265.
9. C. Dong and J. Lepowsky, A Jacobi identity for relative vertex operators and the equivalence of Z-algebras and parafermion algebras, in Proc. XVIIth Intl. Colloq. on Group Theoretical Methods in Physics, Ste-Adéle, June, 1988, eds. Y. Saint-Aubin and L. Vinet, World Scientific, Singapore (1989), pp. 235-238.
10. C. Dong and J. Lepowsky, Generalized Vertex Algebras and Relative Vertex Operators, Progress in Math. Vol. 112, Birkhaüser, Boston (1993).
11. C. Dong and J. Lepowsky, The algebraic structure of relative twisted vertex operators, J. Pure and Applied Algebra 110 (1996) 259-295.
12. C. Dong, H.-S. Li and G. Mason, Simple currents and extensions of vertex operator algebras, Commun. Math. Phys. 180 (1996) 671-707.
13. C. Dong, H.-S. Li and G. Mason, Regularity of rational vertex operator algebras, Adv. Math. 132 (1997) 148-166.
14. C. Dong and G. Mason, Coset constructions and dual pairs for vertex operator algebras, math.QA/9904155.
15. B. Feigin and E. Frenkel, Duality in W-algebras, Internal. Math. Res. Notices 6 (1991) 75-82.
16. (1), Contemporary Math. 121 (1991).
17. I. Frenkel, Y.-Z. Huang and J. Lepowsky, On axiomatic approaches to vertex operator algebras and modules, Memoirs Amer. Math. Soc. 104 (1993).
18. I. Frenkel, J. Lepowsky and A. Meurman, Vertex Operator Algebras and the Monster, Pure and Appl. Math. Vol. 134, Academic Press, Boston (1988).
19. J. Fuchs and C. Schweigert, The action of outer automorphisms on bundles of chiral blocks, Commun. Math. Phys. 206 (1999) 691-736.
20. I. Frenkel and Y.-C. Zhu, Vertex operator algebras associated to representations of affine and Virasoro algebras, Duke Math. J. 66 (1992) 123-168.
21. D. Gepner, New conformal field theories associated with Lie algebras and their partition functions, Nucl. Phys. B290 (1987) 10-24.
22. P. Goddard, A. Kent and D. Olive, Virasoro algebras and coset space models, Phys. Lett. B152 (1985) 88.
23. P. Goddard, A. Kent and D. Olive, Unitary representations of the Virasoro algebra and super-Virasoro algebras, Commun. Math. Phys. 103 (1986) 105-119.
24. Y.-C. Gao and H.-S. Li, Generalized vertex algebras generated by parafermion-like operators, to appear.
25. (1)-modules, Ph.D. thesis, Rutgers University, 1990
26. and Memoirs American Math. Soc. 507 (1993).
27. V. G. Kac, Infinite-Dimensional Lie Algebras, 3rd ed. Cambridge University Press, Cambridge (1990).
28. J. Lepowsky, Rutgers Lecture Notes on Vertex Operator Algebras, Spring (1993).
29. H.-S. Li, Symmetric invariant bilinear forms on vertex operator algebras, J. Pure Appl. Algebra 96 (1994) 279-297.
30. H.-S. Li, Local systems of vertex operators, vertex superalgebras and modules, hep-th/9406185; J. Pure Appl. Algebra 109 (1996) 143-195.
31. H.-S. Li, Local systems of twisted vertex operators, vertex superalgebras and twisted modules, Contemporary Math. 193 (1996) 203-236.
32. H.-S. Li, The physics supers election principle in vertex operator algebra theory, J. Algebra 196 (1997) 436-457.
33. H.-S. Li, Extensions of vertex operator algebras by a self-dual simple modules, J. Algebra 187 (1997) 236-267.
34. H.-S. Li, Certain extensions of vertex operator algebras of affine type, Commun. Math. Phys. 217 (2001) 653-696.
35. H.-S. Li, Regular representations of vertex operator algebras, to appear; Math.QA/9908108.
36. J. Lepowsky and M. Prime, Standard modules for type one affine Lie algebras, in Number Theory, New York, 1982, Lecture Notes in Math. Vol. 1052, Springer-Verlag (1984), pp. 194-251.
37. (1) Contemporary Math. 46 (1985).
38. (1)-modules in the homogeneous picture, in Vertex Operators in Mathematics and Physics, Proc. 1983 M.S.R.I. Conference, eds. J. Lepowsky, S. Mandelstam and I. M. Singer, Publ. Math. Sciences Res. Ins. No. 3, Springer-Verlag, New York (1985), pp. 143-162.
39. (1), Commun. Math. Phys. 62 (1978) 43-53.
40. J. Lepowsky and R. L. Wilson, The Rogers-Ramanujan identities: Lie theoretic interpretation and proof, Proc. Natl. Acad. Sci. USA 78 (1981) 699-701.
41. J. Lepowsky and R. L. Wilson, A Lie theoretic interpretation and proof of the Rogers-Ramanujan identities, Adv. Math. 45 (1982) 21-72.
42. J. Lepowsky and R. L. Wilson, A new family of algebras underlying the Rogers-Ramanujan identities and generalization, Proc. Natl. Acad. Sci. USA 78 (1981) 7254-7258.
43. J. Lepowsky and R. L. Wilson, The structure of standard modules, I: Universal algebras and the Rogers-Ramanujan identities, Invent. Math. 77 (1984) 199-290.
44. (1), principal gradation, Invent. Math. 79 (1985) 417-442.
45. J. Lepowsky and R. L. Wilson, Z-algebras and the Rogers-Ramanujan identities, in Vertex Operators in Mathematics and Physics, Proc. 1983 M.S.R.I. Conference, eds. J. Lepowsky, S. Mandelstam and I. M. Singer, Publ. Math. Sciences Res. Ins. No. 3, Springer-Verlag, New York (1985), pp. 97-142.
46. H.-S. Li and X.-P. Xu, A characterization of vertex algebras associated to even lattices, J. of Algebra 173 (1995) 253-270.
47. (1), Memoirs American Math. Soc. 362 (1987).
48. K. C. Misra, Realization of the level two standard sl(2k +1, C)-modules, Tran. Amer. Math. Soc. 316 (1989) 295-309.
49. 2k+1-moaule.s, Iran. Amer. Math. Soc. 321 (1990) 483-504.
50. K. C. Misra, Level one standard modules for affine symplectic Lie algebras, Math. Ann. 287 (1990) 287-302.
51. n-modules, J. Algebra 137 (1991) 56-76.
52. G. Mossberg, Axiomatic vertex algebras and the Jacobi identity, Ph.D dissertation, University of Lund, Sweden, 1993;
53. Axiomatic vertex algebras and the Jacobi identity, J. Algebra 170 (1994) 956-1010.
54. A. Meurman and M. Prime, Annihilating ideals of standard modules of sl(2, C) and combinatorial identities, Adv. Math. 64 (1987) 177-240.
55. A. Meurman and M. Prime, Annihilating Fields of Standard Modules of sl(2, C) and Combinatorial Identities, Memoirs Amer. Math. Soc. 652 (1999).
56. (1), in Infinite Dimensional Lie Algebras and Groups, Advanced Series in Math. Physics, Vol. 7, ed. V. Kac, World Scientific, Singapore (1989), pp. 273-282.
57. G. Segal, Unitary representations of some infinite-dimensional groups, Commun. Math. Phys. 80 (1981) 301-342.
58. H. Sugawara, A field theory of currents, Phys. Rev. 170 (1968) 1659-1662.
59. N-symmetric statistical systems, Sov. Phys. JETP 62 (1985) 215-225.
60. A. B. Zamolodchikov and V. A. Fateev, Disorder fields in two-dimensional conformal quantum field theory and N = 2 extended supersymmetry, Sov. Phys. JETP 63 (1986) 913-919.
61. Y. Zhu, Talk given in Conformal Field Theory Seminar, Rutgers (1993).