Zhu's algebras, C2-algebras and abelian radicals
Abstract
This paper consists of three parts. In the first part we prove that Zhu's and C2-algebras in type A have the same dimensions. In the second part we compute the graded decomposition of the C2-algebras in type A, thus proving the Gaberdiel-Gannon's conjecture. Our main tool is the theory of abelian radicals, which we develop in the third part.
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