ADE subalgebras of the triplet vertex algebra W(p): D_m-series
Drazen Adamovic, Xianzu Lin, Antun Milas

TL;DR
This paper classifies modules and analyzes algebraic structures of ADE subalgebras of the triplet vertex algebra W(p), focusing on the dihedral series, and establishes properties like C2-cofiniteness and modularity.
Contribution
It introduces a classification of irreducible modules for ADE subalgebras, constructs twisted modules, and proves C2-cofiniteness for all dihedral series cases.
Findings
Classified irreducible modules for $ar{M(1)}^+$ and $ riplet^{D_2}$
Established C2-cofiniteness for all $ riplet^{D_m}$
Computed characters and modular properties of modules
Abstract
We are continuing our study of ADE-orbifold subalgebras of the triplet vertex algebra W(p). This part deals with the dihedral series. First, subject to a certain constant term identity, we classify all irreducible modules for the vertex algebra , the --orbifold of the singlet vertex algebra . Then we classify irreducible modules and determine Zhu's and --algebra for the vertex algebra . A general method for construction of twisted --modules is also introduced. We also discuss classification of twisted --modules including the twisted Zhu's algebra , which is of independent interest. The category of admissible -twisted -modules is expected to be semisimple. We also prove -cofiniteness of for all , and give a conjectural list of irreducible…
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Topics in Algebra · Homotopy and Cohomology in Algebraic Topology
