Simplicity of a vertex operator algebra whose Griess algebra is the Jordan algebra of symmetric matrices
| dc.creator | Niibori, Hidekazu | |
| dc.creator | Sagaki, Daisuke | |
| dc.date | 2009-01-07 | |
| dc.date.accessioned | 2026-07-07T12:27:10Z | |
| dc.date.available | 2026-07-07T12:27:10Z | |
| dc.description | Let $r \in \BC$ be a complex number, and $d \in \BZ_{\ge 2}$ a positive integer greater than or equal to 2. Ashihara and Miyamoto introduced a vertex operator algebra $\Vam$ of central charge $dr$, whose Griess algebra is isomorphic to the simple Jordan algebra of symmetric matrices of size $d$. In this paper, we prove that the vertex operator algebra $\Vam$ is simple if and only if $r$ is not an integer. Further, in the case that $r$ is an integer (i.e., $\Vam$ is not simple), we give a generator system of the maximal proper ideal $I_{r}$ of the VOA $\Vam$ explicitly. | |
| dc.description | 30 pages, no figure | |
| dc.identifier | https://arxiv.org/abs/0901.0841 | |
| dc.identifier | http://arxiv.org/abs/0901.0841 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/215118 | |
| dc.subject | Quantum Algebra | |
| dc.subject | 17B69, 17C99 | |
| dc.title | Simplicity of a vertex operator algebra whose Griess algebra is the Jordan algebra of symmetric matrices | |
| dc.type | text |