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arxiv: 1212.6771 · v1 · submitted 2012-12-30 · 🧮 math.QA · math.RT

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C₂-cofinite W-algebras and their logarithmic representations

Drazen Adamovic , Antun Milas
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keywords algebraslogarithmicmathcaltheorymodulesresultssometriplet
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We discuss our recent results on the representation theory of $\mathcal{W}$--algebras relevant to Logarithmic Conformal Field Theory. First we explain some general constructions of $\mathcal{W}$-algebras coming from screening operators. Then we review the results on $C_2$--cofiniteness, the structure of Zhu's algebras, and the existence of logarithmic modules for triplet vertex algebras. We propose some conjectures and open problems which put the theory of triplet vertex algebras into a broader context. New realizations of logarithmic modules for $\mathcal{W}$-algebras defined via screenings are also presented.

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  1. Derivations on the triplet $W$-algebras with $\mathfrak{sl}_2$-symmetry

    math-ph 2026-04 unverdicted novelty 6.0

    Derivations on triplet W-algebras W_{p+,p-} are built by refining Tsuchiya-Wood Frobenius homomorphisms, extending Adamovic-Milas properties, inducing sl2 symmetry naturally, and yielding Aut(SW(m)) = PSL2(C) x Z2 for...