ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

7. Lie Groups and Lie Algebras

1991 MS Classification: 17B69; 11F03, 11F22, 20D08, 57M99, 81T40, 94B05 Höhn, Gerald, Universität Freiburg Vertex Operator Algebras and 3-dimensional Topological Quantum Field Theories The 3-dimensional topological quantum field theory (3d-TQFT) belonging to a vertex operator algebra (VOA) can be considered as a generalisation of the classical notion of the genus of a quadratic form. We will discuss different aspects of this generalisation, some of them are indicated in the following table of analogies:

general analogies

quadratic form  VOA
genus  3d-TQFT & rank
class number  class number
theta series  correlation functions
codes over abelian groups codes over 3d-TQFTs

analogies between special objects

(shorter) Leech lattice  (shorter) moonshine module
Conway groups  (Baby) Monster
Niemeier classification  list of Schellekens
lattices with long shadows SVOAs with long shadows