Advertisement

Algebras and Representation Theory

, Volume 20, Issue 2, pp 313–334 | Cite as

Characterizations of the Vertex Operator Algebras \({V_{L}^{T}}\) and \({V_{L}^{O}}\)

  • Xianzu Lin
Article
  • 57 Downloads

Abstract

In this paper, we give characterizations of the rational vertex operator algebras \({V_{L}^{T}}\) and \({V_{L}^{O}}\), where L is the root lattice of type A 1, T is the tetrahedral group, and O is the octahedral group. By these two characterizations, the classification of rational VOAs of central charge 1 is reduced to the characterization of \({V_{L}^{I}}\) where I is the icosahedral group.

Keywords

Characterization Rational vertex operator algebra Generators and relations 

Mathematics Subject Classification (2010)

17B69 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Adamović, D.: Classification of irreducible modules of certain subalgebras of free boson vertex algebra. J. Algebra 270, 115–132 (2003)MathSciNetCrossRefMATHGoogle Scholar
  2. 2.
    Adamović, D., Lin, X., Milas, A.: ADE subalgebras of the triplet vertex algebra \(\mathcal {W}(p)\): A m-series. Commun. Contemp. Math. 15, 1350028 (2013)MathSciNetCrossRefMATHGoogle Scholar
  3. 3.
    Adamović, D., Lin, X., Milas, A.: ADE subalgebras of the triplet vertex algebra \(\mathcal {W}(p)\): E 8, preprintGoogle Scholar
  4. 4.
    Adamović, D., Milas, A.: Logarithmic intertwining operators and W(2,2p−1)-algebras. J. Math. Phys. 48, 073503 (2007)MathSciNetCrossRefMATHGoogle Scholar
  5. 5.
    Adamović, D., Milas, A.: On the triplet vertex algebra W(p). Advances Math. 217, 2664–2699 (2008)MathSciNetCrossRefMATHGoogle Scholar
  6. 6.
    Dong, C., Jiang, C.: A Characetrization of Vertex Operator Algebra L(1/2,0)⊗L(1/2,0). Comm. Math. Phys. 296, 69–88 (2010)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Dong, C., Jiang, C.: A characterization of the rational vertex operator algebra \(V_{\mathbb {Z} \alpha }^{+} \): I. arXiv:1110.1882
  8. 8.
    Dong, C., Jiang, C.: A characterization of the rational vertex operator algebra \( V_{\mathbb {Z} \alpha }^{+} \): II. Advances Math. 247, 41–70 (2013)MathSciNetCrossRefMATHGoogle Scholar
  9. 9.
    Dong, C., Jiang, C.: A characterization of the vertex operator algebra \( V^{A4}_{L_{2}}\). arXiv:1310.7236
  10. 10.
    Dong, C., Lin, X., Ng, S.-H.: Congruence Property In Conformal Field Theory (2012). arXiv:1201.6644
  11. 11.
    Dong, C., Mason, G.: Rational vertex operator algebras and the effective central charge, International. Int. Math. Res. Not. 86, 2989–3008 (2004)CrossRefMATHGoogle Scholar
  12. 12.
    Kac, V.G.: Infinite-dimensional Lie algebras, Third edition. Cambridge University Press (1990)Google Scholar
  13. 13.
    Kiritsis, E.: Proof of the completeness of the classification of rational conformal field theories with c=1. Phys. Lett. B217, 427–430 (1989)CrossRefGoogle Scholar
  14. 14.
    Lepowsky, J., Li, H.: Introduction to Vertex Operator Algebras and Their Representations, Progress in Mathematics, vol. 227. Birkhäuser, Boston (2003)Google Scholar
  15. 15.
    Lin, X.: ADE subalgebras of the triplet vertex algebra \(\mathcal {W}(p)\): E 6, E 7. Int. Math. Res. Not. 15, 6752–6792 (2015)CrossRefMATHGoogle Scholar
  16. 16.
    Lin, X.: Fusion rules of Virasoro Vertex Operator Algebras. Proc. Amer. Math. Soc. 143(9), 3765–3776 (2015)MathSciNetCrossRefMATHGoogle Scholar
  17. 17.
    Milas, A.: Fusion rings for degenerate minimal models. J. of Algebra 254, 300–335 (2002)MathSciNetCrossRefMATHGoogle Scholar
  18. 18.
    Roitman, M.: On free conformal and vertex algebras. J. Algebra 217(2), 496–527 (1999)MathSciNetCrossRefMATHGoogle Scholar
  19. 19.
    Serre, J.-P., Stark, H.: Modular forms of weight 1/2. Lect. Notes Math. 627, 27–67 (1971)CrossRefGoogle Scholar
  20. 20.
    Zhu, Y.-C.: Modular invariance of characters of vertex operator algebras. J. Amer. Math. Soc. 9, 237–302 (1996)MathSciNetCrossRefMATHGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2016

Authors and Affiliations

  1. 1.College of Mathematics and Computer ScienceFujian Normal UniversityFuzhouChina

Personalised recommendations