The group of symmetries of the shorter Moonshine module

Höhn, Gerald

doi:10.1007/s12188-010-0040-1

Cited by 27 publications

(27 citation statements)

References 14 publications

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“…Since τ e 0 τ e 1 = ξ u we get {ξ u τ e 0 , ξ 2 u τ e 0 } = {τ e 1 , τ e 2 }. Thus, ge 0 ∈ {e 0 , e 1 , e 2 } by the one-to-one correspondence [Mi1,Hö]. Similarly, we also have ge 1 ∈ {e 0 , e 1 , e 2 } and ge 2 ∈ {e 0 , e 1 , e 2 }.…”

Section: The 3-transposition Propertymentioning

confidence: 85%

McKay’s E7 Observation on the Baby Monster

Höhn

Lam

2011

International Mathematics Research Notices

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In this paper, we study McKay's E 7 observation on the Baby Monster. By investigating so called derived c = 7/10 Virasoro vectors, we show that there is a natural correspondence between dihedral subgroups of the Baby Monster and certain subalgebras of the Baby Monster vertex operator algebra which are constructed by the nodes of the affine E 7 diagram. This allows us to reinterpret McKay's E 7 observation via the theory of vertex operator algebras.For a class of vertex operator algebras including the Moonshine module, we will show that the product of two Miyamoto involutions associated to derived c = 7/10 Virasoro vectors in certain commutant vertex operator algebras is an element of order at most 4. For the case of the Moonshine module, we obtain the Baby monster vertex operator algebra as the commutant and we can identify the group generated by these Miyamoto involutions with the Baby Monster and recover the {3, 4}transposition property of the Baby Monster in terms of vertex operator algebras.

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Section: The 3-transposition Propertymentioning

confidence: 85%

McKay’s E7 Observation on the Baby Monster

Höhn

Lam

2011

International Mathematics Research Notices

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“…The even shorter moonshine vertex operator algebra constructed by Höhn [25] also turns out to be strongly local being a subVOA of V ♮ . Moreover, the automorphism group of the corresponding conformal net coincides the VOA automorphism group which is known to be the Baby Monster group B, the second largest among the sporadic finite simple groups.…”

Section: From Voas To Conformal Nets and Backmentioning

confidence: 89%

Operator algebras and vertex operator algebras

Carpi

2017

The Fourteenth Marcel Grossmann Meeting

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In two-dimensional conformal field theory (CFT) the building blocks are given by chiral CFTs, i.e. CFTs on the unit circle (compactified light-ray). They are generated by quantum fields depending on one light-ray coordinate only. There are two mathematical formulations of chiral CFT, the one based on vertex operator algebras (VOAs) and the one based on conformal nets. We describe some recent results which, for first time, gives a general construction of conformal nets from (unitary) VOAs.

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“…The even shorter moonshine vertex operator algebra constructed by Höhn [10] also turns out to be strongly local being a subVOA of V . Moreover, the automorphism group of the corresponding conformal net coincides the VOA automorphism group which is known to be the baby monster group B.…”

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confidence: 89%