The structure of Zhu's algebras for certain W-algebras

  • Adamocvi D
  • Milas A
  • 4


    Mendeley users who have this article in their library.
  • 11


    Citations of this article.


We introduce a new approach that allows us to determine the structure of Zhu's algebra for certain vertex operator (super)algebras which admit horizontal Z{double-struck}-grading. By using this method and an earlier description of Zhu's algebra for the singlet W-algebra, we completely describe the structure of Zhu's algebra for the triplet vertex algebra W(p). As a consequence, we prove that Zhu's algebra A(W(p)) and the related Poisson algebra P(W(p)) have the same dimension. We also completely describe Zhu's algebras for the N=1 triplet vertex operator superalgebra SW(m). Moreover, we obtain similar results for the c=0 triplet vertex algebra W2,3, important in logarithmic conformal field theory. Because our approach is "internal" we had to employ several constant term identities for purposes of getting right upper bounds on dim(A(V)).This work is, in a way, a continuation of the results published in Adamovǐ and Milas (2008) [4]. © 2011 Elsevier Inc.

Author-supplied keywords

  • Logarithmic conformal field theory
  • Vertex algebras
  • W-algebras
  • Zhu's algebras

Get free article suggestions today

Mendeley saves you time finding and organizing research

Sign up here
Already have an account ?Sign in

Find this document


Cite this document

Choose a citation style from the tabs below

Save time finding and organizing research with Mendeley

Sign up for free