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Article

Zhu's algebras, C_2-algebras and abelian radicals

Journal of Algebra. 2011. Vol. 329. P. 130-146.
Feigin B. L., Feigin E., Littelmann P.

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.