scholarly journals Weyl groups and vertex operator algebras generated by Ising vectors satisfying the (2B, 3C) condition

2014 ◽  
Vol 26 (06) ◽  
pp. 1450011
Author(s):  
Hsian-Yang Chen ◽  
Ching Hung Lam
Keyword(s):  
Weyl Group ◽  
Root System ◽  
Vertex Operator ◽  
Operator Algebras ◽  
Central Charge ◽  
Type A ◽  
Weyl Groups ◽  
Vertex Operator Algebras

In this paper, we construct explicitly certain moonshine type vertex operator algebras generated by a set of Ising vectors I such that (1) for any e ≠ f ∈ I, the subVOA VOA (e, f) generated by e and f is isomorphic to either U2B or U3C; and (2) the subgroup generated by the corresponding Miyamoto involutions {τe | e ∈ I} is isomorphic to the Weyl group of a root system of type An, Dn, E6, E7 or E8. The structures of the corresponding vertex operator algebras and their Griess algebras are also studied. In particular, the central charge of these vertex operator algebras are determined.

scholarly journals Construction and classification of holomorphic vertex operator algebras

2020 ◽  
Vol 2020 (759) ◽  
pp. 61-99 ◽  
Author(s):  
Jethro van Ekeren ◽  
Sven Möller ◽  
Nils R. Scheithauer
Keyword(s):  
Vertex Operator ◽  
Operator Algebras ◽  
Central Charge ◽  
Field Theories ◽  
Vertex Operator Algebras ◽  
Conformal Field Theories ◽  
Cyclic Groups ◽  
Conformal Field

AbstractWe develop an orbifold theory for finite, cyclic groups acting on holomorphic vertex operator algebras. Then we show that Schellekens’ classification of {V_{1}}-structures of meromorphic conformal field theories of central charge 24 is a theorem on vertex operator algebras. Finally, we use these results to construct some new holomorphic vertex operator algebras of central charge 24 as lattice orbifolds.

scholarly journals GENUS-ZERO MODULAR FUNCTORS AND INTERTWINING OPERATOR ALGEBRAS

1998 ◽  
Vol 09 (07) ◽  
pp. 845-863 ◽  
Author(s):  
YI-ZHI HUANG
Keyword(s):  
Vertex Operator ◽  
Operator Algebra ◽  
Vertex Operator Algebra ◽  
Operator Algebras ◽  
Central Charge ◽  
Vertex Operator Algebras ◽  
Main Step ◽  
Group Representations ◽  
Genus Zero ◽  
Intertwining Operator

In [7] and [9], the author introduced the notion of intertwining operator algebra, a nonmeromorphic generalization of the notion of vertex operator algebra involving monodromies. The problem of constructing intertwining operator algebras from representations of suitable vertex operator algebras was solved implicitly earlier in [5]. In the present paper, we generalize the geometric and operadic formulation of the notion of vertex operator algebra given in [3, 4, 11, 12, 8] to the notion of intertwining operator algebra. We show that the category of intertwining operator algebras of central charge [Formula: see text] is isomorphic to the category of algebras over rational genus-zero modular functors (certain analytic partial operads) of central charge c satisfying a certain generalized meromorphicity property. This result is one main step in the construction of genus-zero conformal field theories from representations of vertex operator algebras announced in [7]. One byproduct of the proof of the present isomorphism theorem is a geometric construction of (framed) braid group representations from intertwining operator algebras and, in particular, from representations of suitable vertex operator algebras.

scholarly journals Dimension Formulae in Genus Zero and Uniqueness of Vertex Operator Algebras

2018 ◽  
Vol 2020 (7) ◽  
pp. 2145-2204 ◽  
Author(s):  
Jethro van Ekeren ◽  
Sven Möller ◽  
Nils R Scheithauer
Keyword(s):  
Vertex Operator ◽  
Vertex Operator Algebra ◽  
Operator Algebras ◽  
Central Charge ◽  
Vertex Operator Algebras ◽  
Genus Zero ◽  
Dimension Formula ◽  
Weight One ◽  
Zero Group ◽  
Orbifold Construction

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 and central charge 24: $A_{5}C_{5}E_{6,2}$, $A_{3}A_{7,2}{C_{3}^{2}}$, $A_{8,2}F_{4,2}$, $B_{8}E_{8,2}$, ${A_{2}^{2}}A_{5,2}^{2}B_{2}$, $C_{8}{F_{4}^{2}}$, $A_{4,2}^{2}C_{4,2}$, $A_{2,2}^{4}D_{4,4}$, $B_{5}E_{7,2}F_{4}$, $B_{4}{C_{6}^{2}}$, $A_{4,5}^{2}$, $A_{4}A_{9,2}B_{3}$, $B_{6}C_{10}$, $A_{1}C_{5,3}G_{2,2}$, and $A_{1,2}A_{3,4}^{3}$.

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