The University of Arizona
Please note that this event has ended!

Niemeier Lattices and Holomorphic VOAs of Central Charge 24

Algebra and Number Theory Seminar

Niemeier Lattices and Holomorphic VOAs of Central Charge 24
Series: Algebra and Number Theory Seminar
Location: ENR2 S395
Presenter: Sven Möller, Rutgers University

We prove a systematic construction of all 70 strongly rational,
holomorphic VOAs $V$ of central charge 24 with non-zero weight-one space
$V_1$ as cyclic orbifold constructions associated with the 24 Niemeier
lattice VOAs $V_N$ and certain 230 "good" automorphisms of small order
in $\Aut(V_N)$.

We show that up to algebraic conjugacy these automorphisms are exactly
the generalised deep holes, as introduced in [Möller-Scheithauer-2019],
of the Niemeier lattice VOAs with the additional property that their
orders are equal to those of the corresponding outer automorphisms.

Together with the constructions in [Höhn-2017] and
[Möller-Scheithauer-2019] this gives three different *uniform*
constructions of these VOAs, which are however related through 11
algebraic conjugacy classes in $\Co_0$.

Finally, by considering the inverse orbifold constructions associated
with the 230 "good" automorphisms, we give the first *uniform* proof of
the fact that each strongly rational, holomorphic VOA $V$ of central
charge 24 with non-zero weight-one space $V_1$ is uniquely determined by
the Lie algebra structure of $V_1$.

This is joint work with Gerald Höhn.