# INERTIA GROUPS AND UNIQUENESS OF HOLOMORPHIC VERTEX OPERATOR ALGEBRAS

@article{Lam2020INERTIAGA, title={INERTIA GROUPS AND UNIQUENESS OF HOLOMORPHIC VERTEX OPERATOR ALGEBRAS}, author={Ching Hung Lam and Hiroki Shimakura}, journal={Transformation Groups}, year={2020}, volume={25}, pages={1223-1268} }

We continue our program on classiffication of holomorphic vertex operator algebras of central charge 24. In this article, we show that there exists a unique strongly regular holomorphic VOA of central charge 24, up to isomorphism, if its weight one Lie algebra has the type C 4,10 , D 7,3 A 3,1 G 2,1 , A 5,6 C 2,3 A 1,2 , A 3,1 C 7,2 , D 5,4 C 3,2 A A 1 , 1 2 $$ {A}_{1,1}^2 $$ , or E 6,4 C 2,1 A 2,1 . As a consequence, we have verified that the isomorphism class of a strongly regular holomorphic…

## 7 Citations

Systematic Orbifold Constructions of Schellekens' Vertex Operator Algebras from Niemeier Lattices

- Mathematics
- 2020

We present a systematic, rigorous construction of all 70 strongly rational, holomorphic vertex operator algebras V of central charge 24 with non-zero weight-one space V1 as cyclic orbifold…

Systematic orbifold constructions of Schellekens' vertex operator algebras from Niemeier lattices

- MathematicsJournal of the London Mathematical Society
- 2022

We present a systematic, rigorous construction of all 70 strongly rational, holomorphic vertex operator algebras $V$ of central charge 24 with non-zero weight-one space $V_1$ as cyclic orbifold…

A lattice theoretical interpretation of generalized deep holes of the Leech lattice vertex operator algebra

- Mathematics
- 2022

We give a lattice theoretical interpretation of generalized deep holes of the Leech lattice VOA V Λ . We show that a generalized deep hole deﬁnes a “true” automorphism invariant deep hole of the…

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

- MathematicsLetters in Mathematical Physics
- 2019

Let L be an even (positive definite) lattice and $$g\in O(L)$$ g ∈ O ( L ) . In this article, we prove that the orbifold vertex operator algebra $$V_{L}^{{\hat{g}}}$$ V L g ^ has group-like fusion if…

A Short Introduction to the Algebra, Geometry, Number Theory and Physics of Moonshine

- Mathematics
- 2020

Moonshine arose in the 1970s as a collection of coincidences connecting modular functions to the monster simple group, which was newly discovered at that time. The effort to elucidate these…

Orbifold vertex operator algebras associated with coinvariant lattices of Leech lattice

- Mathematics
- 2018

We prove that the orbifold vertex operator algebra $V_{L_g}^{\hat{g}}$ associated with the coinvariant lattice of a unimodular lattice $L$ and an isometry $g\in O(L)$ has group-like fusion. We also…

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Abstract In this paper, we study orbifold constructions associated with the Leech lattice vertex operator algebra. As an application, we prove that the structure of a strongly regular holomorphic…

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In this thesis we develop an orbifold theory for a finite, cyclic group G acting on a suitably regular, holomorphic vertex operator algebra V. To this end we describe the fusion algebra of the…

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