Automorphism group of an orbifold vertex operator algebra associated with the Leech lattice

2020 ◽  
pp. 127-138
Author(s):  
Ching Lam
Keyword(s):  
Automorphism Group ◽  
Vertex Operator ◽  
Operator Algebra ◽  
Vertex Operator Algebra ◽  
Leech Lattice

scholarly journals THE MOONSHINE MODULE FOR CONWAY’S GROUP

2015 ◽  
Vol 3 ◽  
Author(s):  
JOHN F. R. DUNCAN ◽  
SANDER MACK-CRANE
Keyword(s):  
Automorphism Group ◽  
Fixed Points ◽  
Vertex Operator ◽  
Operator Algebra ◽  
Fourier Expansion ◽  
Vertex Operator Algebra ◽  
Natural Analogue ◽  
Genus Zero ◽  
Leech Lattice ◽  
Special Case

We exhibit an action of Conway’s group – the automorphism group of the Leech lattice – on a distinguished super vertex operator algebra, and we prove that the associated graded trace functions are normalized principal moduli, all having vanishing constant terms in their Fourier expansion. Thus we construct the natural analogue of the Frenkel–Lepowsky–Meurman moonshine module for Conway’s group. The super vertex operator algebra we consider admits a natural characterization, in direct analogy with that conjectured to hold for the moonshine module vertex operator algebra. It also admits a unique canonically twisted module, and the action of the Conway group naturally extends. We prove a special case of generalized moonshine for the Conway group, by showing that the graded trace functions arising from its action on the canonically twisted module are constant in the case of Leech lattice automorphisms with fixed points, and are principal moduli for genus-zero groups otherwise.

scholarly journals The automorphism group of the -orbifold of the Barnes–Wall lattice vertex operator algebra of central charge 32

2014 ◽  
Vol 156 (2) ◽  
pp. 343-361 ◽  
Author(s):  
HIROKI SHIMAKURA
Keyword(s):  
Automorphism Group ◽  
Vertex Operator ◽  
Operator Algebra ◽  
Vertex Operator Algebra ◽  
Central Charge ◽  
Group Structure ◽  
Graph Structure ◽  
Full Automorphism Group ◽  
Lattice Vertex Operator Algebra

AbstractIn this paper, we prove that the full automorphism group of the ${\mathbb Z}_2$-orbifold of the Barnes–Wall lattice vertex operator algebra of central charge 32 has the shape 227.E6(2). In order to identify the group structure, we introduce a graph structure on the Griess algebra and show that it is a rank 3 graph associated to E6(2).

scholarly journals On orbifold constructions associated with the Leech lattice vertex operator algebra

2018 ◽  
Vol 168 (2) ◽  
pp. 261-285 ◽  
Author(s):  
CHING HUNG LAM ◽  
HIROKI SHIMAKURA
Keyword(s):  
Lie Algebra ◽  
Vertex Operator ◽  
Operator Algebra ◽  
Vertex Operator Algebra ◽  
Operator Algebras ◽  
Central Charge ◽  
Leech Lattice ◽  
Weight One ◽  
Strongly Regular ◽  
Lattice Vertex Operator Algebra

AbstractIn 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 vertex operator algebra of central charge 24 is uniquely determined by its weight one Lie algebra if the Lie algebra has the type A3,43A1,2, A4,52, D4,12A2,6, A6,7, A7,4A1,13, D5,8A1,2 or D6,5A1,12 by using the reverse orbifold construction. Our result also provides alternative constructions of these vertex operator algebras (except for the case A6,7) from the Leech lattice vertex operator algebra.

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