The structure of Zhu's algebras for certain \(\mathcal W\)-algebras

DOI10.1016/j.aim.2011.05.007zbMath1302.17041arXiv1006.5134OpenAlexW2963674319MaRDI QIDQ550397

Dražen Adamović, Antun Milas

Publication date: 8 July 2011

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1006.5134

zbMATH Keywords

Zhu algebra\(W\)-algebratripet vertex algebra

Mathematics Subject Classification ID

Vertex operators; vertex operator algebras and related structures (17B69) Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, (W)-algebras and other current algebras and their representations (81R10)

Related Items (23)

On the Feigin-Tipunin conjecture ⋮ The vertex algebras \(\mathcal{R}^{(p)}\) and \(\mathcal{V}^{(p)}\) ⋮ Characters of Modules of Irrational Vertex Algebras ⋮ Logarithmic conformal field theory, log-modular tensor categories and modular forms ⋮ Higgs and Coulomb branches from vertex operator algebras ⋮ The level two Zhu algebra for the Heisenberg vertex operator algebra ⋮ A quasi-Hopf algebra for the triplet vertex operator algebra ⋮ On Zhu's algebra and \(C_2\)-algebra for symplectic fermion vertex algebra \(SF (d)^+\) ⋮ Yoneda algebras of the triplet vertex operator algebra ⋮ Relating the archetypes of logarithmic conformal field theory ⋮ Logarithmic W-algebras and Argyres-Douglas theories at higher rank ⋮ The Level One Zhu Algebra for the Heisenberg Vertex Operator Algebra ⋮ Higher level Zhu algebras and modules for vertex operator algebras ⋮ ADE SUBALGEBRAS OF THE TRIPLET VERTEX ALGEBRA 𝒲(p): D-SERIES ⋮ ${\mathbbm {C}}$ C -Graded vertex algebras and conformal flow ⋮ Classification of screening systems for lattice vertex operator algebras ⋮ SOME REMARKS ON PSEUDO-TRACE FUNCTIONS FOR ORBIFOLD MODELS ASSOCIATED WITH SYMPLECTIC FERMIONS ⋮ ADE SUBALGEBRAS OF THE TRIPLET VERTEX ALGEBRA $\mathcal{W}(p)$: A-SERIES ⋮ The level one Zhu algebra for the Virasoro vertex operator algebra ⋮ On \(\mathcal W\)-algebra extensions of \((2,p)\) minimal models: \(p>3\) ⋮ Logarithmic Tensor Category Theory for Generalized Modules for a Conformal Vertex Algebra, I: Introduction and Strongly Graded Algebras and Their Generalized Modules ⋮ C 2-Cofinite $\mathcal{W}$-Algebras and Their Logarithmic Representations ⋮ An explicit realization of logarithmic modules for the vertex operator algebra $\mathcal {W}_{p,p^{\prime }}$Wp,p′

Cites Work

• Zhu's algebras, \(C_{2}\)-algebras and abelian radicals
• Modular invariance of vertex operator algebras satisfying \(C_2\)-cofiniteness
• On \(\mathcal W\)-algebra extensions of \((2,p)\) minimal models: \(p>3\)
• The \(N = 1\) triplet vertex operator superalgebras
• Logarithmic extensions of minimal models: characters and modular transformations
• The \(N=1\) triplet vertex operator superalgebras: twisted sector
• Kazhdan-Lusztig correspondence for the representation category of the triplet \(W\)-algebra in logarithmic CFT
• Classification of irreducible modules of certain subalgebras of free boson vertex algebra.
• Nonsemisimple fusion algebras and the Verlinde formula
• On the triplet vertex algebra \(\mathcal W(p)\)
• On W-Algebras Associated to (2, p) Minimal Models and Their Representations
• Kazhdan-Lusztig-dual quantum group for logarithimic extensions of Virasoro minimal models
• Logarithmic intertwining operators and W(2,2p−1) algebras
• Zhu's algebra and theC₂-algebra in the symplectic and the orthogonal cases
• Fusion rules and boundary conditions in thec= 0 triplet model
• Modular invariance of characters of vertex operator algebras
• Characters, supercharacters and Weber modular functions
• Zhu's algebra, the C_2 algebra, and twisted modules
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