Construction of Holomorphic Vertex Operator Algebras of Central Charge 24 Using the Leech Lattice and Level p Lattices

Lam, Ching Hung; Shimakura, Hiroki

doi:10.21915/bimas.2017102

Cited by 4 publications

(3 citation statements)

References 24 publications

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“…Remark 5.1. Based on a similar method, some partial results for the conjugacy classes 2A, 3B, 5B and 7B and 2C were obtained in [LS17] and [HS14], respectively. Remark 5.2.…”

Section: Automorphism Groups Of Holomorphic Voas Of Central Charge 24mentioning

confidence: 99%

Automorphism groups and uniqueness of holomorphic vertex operator algebras of central charge $24$

Betsumiya¹,

Lam²,

Shimakura³

2022

Preprint

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We describe the automorphism groups of all holomorphic vertex operator algebras of central charge 24 with non-trivial weight one Lie algebras by using their constructions as simple current extensions. We also confirm a conjecture of G. Höhn on the numbers of holomorphic vertex operator algebras of central charge 24 obtained as inequivalent simple current extensions of certain vertex operator algebras, which gives another proof of the uniqueness of holomorphic vertex operator algebras of central charge 24 with non-trivial weight one Lie algebras.

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“…Remark 5.1. Based on a similar method, some partial results for the conjugacy classes 2A, 3B, 5B and 7B and 2C were obtained in [LS17] and [HS14], respectively. Remark 5.2.…”

Section: Automorphism Groups Of Holomorphic Voas Of Central Charge 24mentioning

confidence: 99%

Automorphism groups and uniqueness of holomorphic vertex operator algebras of central charge $24$

Betsumiya¹,

Lam²,

Shimakura³

2022

Preprint

Self Cite

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“…The following lemma will be used in the computation of quantum dimensions. Note that the case when |g| is a prime has been discussed in [LS17].…”

Section: By the Proposition Above The Modulementioning

confidence: 99%

“…In this section, we will verify his conjecture and prove the following theorem. Recall that the cases for prime order elements have been treated in [LS17] (see also [HS14]) and thus we only consider the cases when |g| is not a prime in this section. Theorem 6.1.…”

Section: Leech Lattice and Some Explicit Examplesmentioning

confidence: 99%

Cyclic orbifolds of lattice vertex operator algebras having group-like fusions

Lam

2019

Lett Math Phys

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Let L be an even (positive definite) lattice and g ∈ O(L). In this article, we prove that the orbifold vertex operator algebra Vĝ L has group-like fusion if and only if g acts trivially on the discriminant group D(L) = L * /L (or equivalently (1 − g)L * < L).We also determine their fusion rings and the corresponding quadratic space structures when g is fixed point free on L. By applying our method to some coinvariant sublattices of the Leech lattice Λ, we prove a conjecture proposed by G. Höhn. In addition, we also discuss a construction of certain holomorphic vertex operator algebras of central charge 24 using the the orbifold vertex operator algebra Vĝ Λg .where wt(·) denotes the conformal weight of the module. Moreover, R(V Lg ) is isomorphic to D(L g ) = L * g /L g as a quadratic space. By some recent results on coset constructions [CKM1, Main Theorem 2] (see also[KMi15] and [Lin17]), it is known that the VOA W also has group-like fusion and R(W ) forms a quadratic space isomorphic to (R(V Lg ), −q), where the quadratic form is defined by conformal weights modulo Z. Since V Lg ⊗ W is a full subVOA of V and V is holomorphic, the VOA V defines a maximal totally singular subspace of R(V Lg ) × R(W ); hence it induces an anti-isomorphism of quadratic spaces ϕ :2 Conversely, let ϕ : (R(V Lg ), q) → (R(W ), −q ′ ) be an isomorphism of quadratic spaces. Then the set {(M, ϕ(M)) | M ∈ R(V Lg )} is a maximal totally singular subspace of R(V Lg ) × R(W ) and hence U = M ∈R(V Lg ) M ⊗ ϕ(M) has a structure of a holomorphic VOA.

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Automorphism Groups and Uniqueness of Holomorphic Vertex Operator Algebras of Central Charge 24

Betsumiya

Lam

Shimakura

2022

Commun. Math. Phys.

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Construction of Holomorphic Vertex Operator Algebras of Central Charge 24 Using the Leech Lattice and Level p Lattices

Cited by 4 publications

References 24 publications

Automorphism groups and uniqueness of holomorphic vertex operator algebras of central charge $24$

Automorphism groups and uniqueness of holomorphic vertex operator algebras of central charge $24$

Cyclic orbifolds of lattice vertex operator algebras having group-like fusions

Automorphism Groups and Uniqueness of Holomorphic Vertex Operator Algebras of Central Charge 24

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