Zhu's algebras, C2-algebras and abelian radicals

Boris Feigin, Evgeny Feigin, Peter Littelmann*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


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 conjecture. Our main tool is the theory of abelian radicals, which we develop in the third part.

Original languageEnglish
Pages (from-to)130-146
Number of pages17
JournalJournal of Algebra
Issue number1
StatePublished - 1 Mar 2011
Externally publishedYes


FundersFunder number
Alexander von Humboldt-Stiftung09-02-12446-ofi-m
Deutsche Forschungsgemeinschaft
Russian Foundation for Basic Research07-02-00799, 09-01-00058, NSh-3472.2008.2


    • C2-algebra
    • Multiplicity free action
    • Spherical variety
    • Vertex operator algebra
    • Zhu's algebra


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