Zhu's algebras, $C_2$-algebras and abelian radicals

Details Zhu's algebras, $C_2$-algebras and abelian radicals Zhu's algebras, $C_2$-algebras and abelian radicals

2009-07-23

arxiv.org/abs/0907.3962v2

Mathematics

Representation Theory

19 pages

Scientific paper

This paper consists of three parts. In the first part we prove that Zhu's and
$C_2$-algebras in type $A$ have the same dimensions. In the second part we
compute the graded decomposition of the $C_2$-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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