Abstract
Let r ∈ ℂ be a complex number, and d ∈ ℤ≥2 a positive integer greater than or equal to 2. Ashihara and Miyamoto [Citation4] introduced a vertex operator algebra V 𝒥 of central charge dr, whose Griess algebra is isomorphic to the simple Jordan algebra of symmetric matrices of size d. In this article, we prove that the vertex operator algebra V 𝒥 is simple if and only if r is not an integer. Further, in the case that r is an integer (i.e., V 𝒥 is not simple), we give a generator system of the maximal proper ideal I r of the VOA V 𝒥 explicitly.
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2000 Mathematics Subject Classification:
ACKNOWLEDGMENTS
The authors would like to express their sincere gratitude to Professor Masahiko Miyamoto, Professor Toshiyuki Abe, Professor Hiroki Shimakura, Professor Hiroshi Yamauchi, and Dr. Takahiro Ashihara for valuable discussions.
Notes
Communicated by D. Nakano.