Regularity of certain vertex operator algebras with two generators
Abstract
For every $m \in {\C} \setminus \{0, 2\}$ and every nonnegative integer $k$ we define the vertex operator (super)algebra $D_{m,k}$ having two generators and rank $ \frac{3 m}{m + 2}$. If $m$ is a positive integer then $D_{m,k}$ can be realized as a subalgebra of a lattice vertex algebra. In this case, we prove that $D_{m,k}$ is a regular vertex operator (super)algebra and find the number of inequivalent irreducible modules.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 November 2001
 arXiv:
 arXiv:math/0111055
 Bibcode:
 2001math.....11055A
 Keywords:

 Quantum Algebra;
 Representation Theory;
 17B69
 EPrint:
 17 pages, Latex