# Seminars & Colloquia Calendar

Lie Group Quantum Mathematics Seminar

## Dimension Formulae in Genus Zero and Uniqueness of Vertex Operator Algebras

#### Sven Moeller, Rutgers University

Location:  HILL 705
Date & time: Friday, 15 September 2017 at 12:00PM - 1:00PM

Abstract :  We prove a dimension formula for orbifold vertex operator algebras of central charge 24 by automorphisms of order $$n$$ such that $$Gamma_0(n)$$ is a genus zero group. We then use this formula together with the inverse orbifold construction for automorphisms of orders 2, 4, 5, 6 and 8 to establish that each of the following fifteen Lie algebras is the weight-one space $$V_1$$ of exactly one holomorphic, $$C_2$$-cofinite vertex operator algebra $$V$$ of CFT-type of central charge 24: $$A_5C_5E_{6,2}$$, $$A_3A_{7,2}C_3^2$$, $$A_{8,2}F_{4,2}$$, $$B_8E_{8,2}$$, $$A_2^2A_{5,2}^2B_2$$, $$C_8F_4^2$$, $$A_{4,2}^2C_{4,2}$$, $$A_{2,2}^4D_{4,4}$$, $$B_5E_{7,2}F_4$$, $$B_4C_6^2$$, $$A_{4,5}^2$$, $$A_4A_{9,2}B_3$$, $$B_6C_{10}$$, $$A_1C_{5,3}G_{2,2}$$ and $$A_{1,2}A_{3,4}^3$$.

This is joint work with Nils Scheithauer (Darmstadt) and Jethro van Ekeren (IMPA, Rio de Janeiro).

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