We establish relations between vertex operator algebras in mathematics and string path integrals in physics. In particular, we construct the basic representations of affine Lie algebras of [italic capitals]ÂD̂Ê-type using a method of string path integrals.
Introduction Actions of matched pairs Cocycles attached to the pentagon equation Multiplicative unitary Kac algebra structure Group-like elements Examples of finite-dimensional Kac algebras Inclusions with the Coxeter-Dynkin graph $D^{(1)}_6$ and the Kac-Paljutkin algebra Struct…
We present a new proof of the identities needed to exhibit an explicit [bold]Z-basis for the universal enveloping algebra associated to an affine Lie algebra. We then use the explicit [bold]Z-bases to extend Borcherds' description, via vertex operator representations, of a [bold…
