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On the triplet vertex algebra W(p) (CROSBI ID 136978)

Prilog u časopisu | izvorni znanstveni rad | međunarodna recenzija

Adamović, Dražen ; Milas, Antun On the triplet vertex algebra W(p) // Advances in mathematics, 217 (2008), 6; 2664-2699-x

Podaci o odgovornosti

Adamović, Dražen ; Milas, Antun

engleski

On the triplet vertex algebra W(p)

We study the triplet vertex operator algebra W(p) of central charge $1-\frac{; ; 6(p-1)^2}; ; {; ; p}; ; $, $p \geq 2$. We show that W(p) is $C_2$-cofinite but irrational since it admits indecomposable and logarithmic modules. Furthermore, we prove that W(p) is of finite-representation type and we provide an explicit construction and classification of all irreducible W(p)-modules and describe block decomposition of the category of ordinary W(p)-modules. All this is done through an extensive use of Zhu's associative algebra together with explicit methods based on vertex operators and the theory of automorphic forms. Moreover, we obtain an upper bound for A(W(p)). Finally, for p prime, we completely describe the structure of A(W(p)). The methods of this paper are easily extendable to other W-algebras and superalgebras.

W-algebras; Vertex algebras; Logarithmic conformal field theory

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Podaci o izdanju

217 (6)

2008.

2664-2699-x

objavljeno

0001-8708

Povezanost rada

Matematika

Poveznice
Indeksiranost