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

Autori
Adamović, Dražen ; Milas, Antun

Izvornik
Advances in mathematics (0001-8708) 227 (2011), 6; 2425-2456

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

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

Sažetak
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.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

POVEZANOST RADA