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The structure of Zhu's algebras for certain W-algebras (CROSBI ID 172093)

Prilog u časopisu | izvorni znanstveni rad | međunarodna recenzija

Adamović, Dražen ; Milas, Antun The structure of Zhu's algebras for certain W-algebras // Advances in mathematics, 227 (2011), 6; 2425-2456. doi: 10.1016/j.aim.2011.05.007

Podaci o odgovornosti

Adamović, Dražen ; Milas, Antun

engleski

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

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-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 W_{; ; ; 2, 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 dimension of Zhu's algebras.

Vertex algebras; Zhu's algebras; W-algebras; logarithmic conformal field theory

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Podaci o izdanju

227 (6)

2011.

2425-2456

objavljeno

0001-8708

10.1016/j.aim.2011.05.007

Povezanost rada

Matematika

Poveznice
Indeksiranost