scholarly journals The automorphism group of the vertex operator algebra VL+ for an even lattice L without roots

2004 ◽  
Vol 280 (1) ◽  
pp. 29-57 ◽  
Author(s):  
Hiroki Shimakura
Keyword(s):  
Automorphism Group ◽  
Vertex Operator ◽  
Operator Algebra ◽  
Vertex Operator Algebra

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 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.

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