Naslov
On the triplet vertex algebra W(p)

Autori
Adamović, Dražen ; Milas, Antun

Izvornik
Advances in Mathematics (0001-8708) 217 (2008), 6; 2664-2699

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

Ključne riječi
W-algebras; Vertex algebras; Logarithmic conformal field theory

Sažetak
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.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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