The irreducible modules and fusion rules for the parafermion vertex operator algebras

DOI10.1090/tran/7302zbMath1433.17034arXiv1412.8154OpenAlexW2962748795MaRDI QIDQ4642531

Chunrui Ai, Li Ren, Xiangyu Jiao, Chongying Dong

Publication date: 23 May 2018

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1412.8154

zbMATH Keywords

irreducible modulesfusion rulesquantum dimensionsparafermion vertex operator algebras

Mathematics Subject Classification ID

Vertex operators; vertex operator algebras and related structures (17B69)

Related Items (29)

Representations of the parafermion vertex operator algebras ⋮ Tensor decomposition, parafermions, level-rank duality, and reciprocity law for vertex operator algebras ⋮ Trace functions of the parafermion vertex operator algebras ⋮ \(G\)-twisted associative algebras of vertex operator superalgebras ⋮ \(S\)-matrix in permutation orbifolds ⋮ Correspondences of categories for subregular \(\mathcal{W}\)-algebras and principal \(\mathcal{W}\)-superalgebras ⋮ Super orbifold theory ⋮ On orbifold theory ⋮ Automorphism group of parafermion vertex operator algebras ⋮ Representations of \(\mathbb{Z}_2\)-orbifold of the parafermion vertex operator algebra \(K(sl_{2},k)\) ⋮ Vertex operator algebras generated by two Ising vectors ⋮ Congruence property in orbifold theory ⋮ Tensor Categories for Vertex Operator Superalgebra Extensions ⋮ On the tensor structure of modules for compact orbifold vertex operator algebras ⋮ The boundary phase transitions of the 2+1D \(\mathbb{Z}_N\) topological order via topological Wick rotation ⋮ Inertia groups and uniqueness of holomorphic vertex operator algebras ⋮ \(S\)-matrix in orbifold theory ⋮ Fusion rules for \(\mathbb{Z}_2\)-orbifolds of affine and parafermion vertex operator algebras ⋮ Sixty-Four Curves of Degree Six ⋮ The VOAs generated by two Ising vectors \(e\) and \(f\) with \(\langle e, f \rangle = \frac{1}{2^8}, |\tau_e \tau_f| = 3\) or \(\langle e, f \rangle = \frac{3}{2^9}\) ⋮ Uniqueness of VOA structure of \(3C\)-algebra and \(5A\)-algebra ⋮ Representations of the orbifold VOAS \(L_{\widehat{\mathfrak{sl}_2}}(k,0)^K\) and the commutant VOAS \(C_{{L_{\widehat{\mathfrak{so}_m}}(1,0)}^{\otimes 3}}({L_{\widehat{\mathfrak{so}_m}}(3,0)})\) ⋮ Representations and fusion rules for the orbifold vertex operator algebras Lsl2̂(k,0)Zp ⋮ Vertex operator superalgebras and the 16-fold way ⋮ \(6A\)-algebra and its representations ⋮ Quantum dimensions and fusion rules for parafermion vertex operator algebras ⋮ The structure of parafermion vertex operator algebras \(K(osp(1|2n),k)\) ⋮ A holomorphic vertex operator algebra of central charge 24 with the weight one Lie algebra \(F_{4,6}A_{2,2}\) ⋮ Parafermion vertex operator algebras and $W$-algebras

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