@article{c1049d311d5c49f3ac87893128ee6f8b,

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

keywords = "C2-algebra, Multiplicity free action, Spherical variety, Vertex operator algebra, Zhu's algebra",

author = "Boris Feigin and Evgeny Feigin and Peter Littelmann",

note = "Funding Information: The work of E.F. was partially supported by the RFBR Grants 09-01-00058, 07-02-00799 and NSh-3472.2008.2, by Pierre Deligne fund based on his 2004 Balzan prize in mathematics and by Alexander von Humboldt Fellowship. The work of B.F. was partially supported by RFBR initiative interdisciplinary project 09-02-12446-ofi-m and by RFBR-CNRS grant 09-02-93106. The work of P.L. was partially supported by the priority program SPP 1377 of the German Science Foundation.",

year = "2011",

month = mar,

day = "1",

doi = "10.1016/j.jalgebra.2010.03.005",

language = "אנגלית",

volume = "329",

pages = "130--146",

journal = "Journal of Algebra",

issn = "0021-8693",

publisher = "Academic Press Inc.",

number = "1",

}