Integral forms in vertex operator algebras, a survey

Document Type : Ischia Group Theory 2018

Author

University of Michigan

Abstract

We give a brief survey of recent work on integral forms in vertex operator algebras (VOAs).

Keywords


[1] Richard E. Borcherds and Alex J. E. Ryba, Modular Moonshine, II., Duke Math. J., 83 (1996) 435–459.
[2] S. Carnahan, Four self-dual integral forms of the moonshine module, arXiv:1710.00737v3, (2018), about 29 pages.
[3] Ch. Dong, R. L., Jr. Griess and A. Ryba, Rank one lattice type vertex operator algebras and their automorphism
groups, II, E-series, J. Algebra, 217 217 (1999) 701–710.
[4] Ch. Dong and R. L., Jr. Griess, The rank-2 lattice-type vertex operator algebras V+L and their automorphism groups, Michigan Math. J., 53 (2005) 691–715.
[5] Ch. Dong and R. L., Jr. Griess, Integral forms in vertex operator algebras which are invariant under finite groups,
J. Algebra, 365 (2012) 184–198.
[6] Ch. Dong and R. L., Jr. Griess, Lattice-integrality of certain group-invariant integral forms in vertex operator
algebras, (English summary) J. Algebra, 474 (2017) 505–516.
[7] I. Frenkel, J. Lepowsky and A. Meurman, Vertex operator algebras and the Monster, Pure and Applied Mathematics, 134, Academic Press, Inc., Boston, MA, 1988.
[8] D. E. Frohardt and R. L., Jr. Griess, Automorphisms of modular Lie algebras, (English summary), Nova J. Algebra
Geom., 1 (1992) 339–345.
[9] R. L., Jr. Griess and Ching Hung Lam, Groups of Lie type, vertex algebras, and modular moonshine, Electron.
Res. Announc. Math. Sci., 21 (2014) 167–176.
[10] R. L., Jr. Griess and Ching Hung Lam, Groups of Lie type, vertex algebras, and modular moonshine, Int. Math.
Res. Not. IMRN, 2015 10716–10755.
[11] M. Miyamoto, Griess algebras and conformal vectors in vertex operator algebras, J. Algebra, 179 (1996) 523–548.
[12] Sh. Sakuma, 6-transposition property of τ -involutions of vertex operator algebras, Int. Math. Res. Not. IMRN,
2007 Art. ID rnm 030, 19 pp.
[13] H. Shimakura, The automorphism group of the vertex operator algebra V+L for an even lattice L without roots, J. Algebra, 280 (2004) 29–57.
[14] H. Shimakura, The automorphism groups of the vertex operator algebras V+L : general case, Math. Z., 252 (2006)
849–862.
[15] G. Simon, Automorphism-invariant Integral Forms in Griess Algebras, doctoral thesis University of Michigan,
2016, https://deepblue.lib.umich.edu/handle/2027.42/133314.
[16] A. J. E. Ryba, Modular Moonshine, article in Moonshine, the Monster, and related topics (South Hadley, MA,
1994), Contemp. Math., 193 307–336, Amer. Math. Soc., Providence, RI, 1996.
Volume 9, Issue 2 - Serial Number 2
Proceedings of the Ischia Group Theory 2018- Part 2
June 2020
Pages 133-138
  • Receive Date: 07 January 2019
  • Revise Date: 04 January 2020
  • Accept Date: 08 January 2020
  • Published Online: 01 June 2020