On the triplet vertex algebra W(p)

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dc.creatorAdamovic, Drazen
dc.creatorMilas, Antun
dc.date2007-07-12
dc.date2007-11-28
dc.date.accessioned2026-07-07T09:25:04Z
dc.date.available2026-07-07T09:25:04Z
dc.descriptionWe study the triplet vertex operator algebra $\mathcal{W}(p)$ of central charge $1-\frac{6(p-1)^2}{p}$, $p \geq 2$. We show that $\trip$ is $C_2$-cofinite but irrational since it admits indecomposable and logarithmic modules. Furthermore, we prove that $\trip$ is of finite-representation type and we provide an explicit construction and classification of all irreducible $\mathcal{W}(p)$-modules and describe block decomposition of the category of ordinary $\trip$-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 ${\rm dim}(A(\mathcal{W}(p)))$. Finally, for $p$ prime, we completely describe the structure of $A(\trip)$. The methods of this paper are easily extendable to other $\mathcal{W}$-algebras and superalgebras.
dc.description32 pages; v2: a few minor changes, to appear in Advances in Mathematics
dc.identifierhttps://arxiv.org/abs/0707.1857
dc.identifierhttp://arxiv.org/abs/0707.1857
dc.identifierAdvances in Mathematics, 217 (2008) 2664-2699.
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/156283
dc.subjectQuantum Algebra
dc.subjectHigh Energy Physics - Theory
dc.subjectMathematical Physics
dc.subjectRepresentation Theory
dc.titleOn the triplet vertex algebra W(p)
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