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Lie Groups Quantum Mathematics Seminar

Cyclic Orbifolds of the Leech Lattice Vertex Operator Algebra

Sven Moeller, Rutgers

Location:  Hill 705
Date & time: Friday, 09 March 2018 at 12:00PM - 1:00PM

Abstract:   Recent results have established that the weight-one space of a (suitably regular) holomorphic VOA of central charge 24 is one of 71 Lie algebras (Schellekens' list) and all of these cases have now been constructed in a joint effort by many authors. The main tool for constructing these VOAs is the orbifold construction, which we established for arbitrary cyclic groups of automorphisms.

In analogy to the construction of all the Niemeier lattices from the Leech lattice (via its deep holes) we conjecture that all 71 cases on Schellekens' list can be obtained in a uniform way as cyclic orbifold constructions from the Leech lattice VOA.

In an ongoing effort we have constructed 63 cases so far. If all 71 cases could be constructed from the Leech lattice VOA in this way, this would greatly help to gain a more conceptual understanding of Schellekens' list. Moreover, this provides evidence for the effectiveness of cyclic orbifolding. (We do believe however that the orbifold theory can and should be extended to more general, in particular non-abelian, groups.)

(This is work in progress joint with Nils Scheithauer)

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