3-transposition Groups of Symplectic Type and Vertex Operator Algebras

9truein 6.5truein BOSONIC CONSTRUCTION OF VERTEX OPERATOR PARA-ALGEBRAS FROM SYMPLECTIC AFFINE KAC-MOODY ALGEBRAS BY MICHAEL DAVID WEINER

Symplectic Fermions – Symmetries of a Vertex Operator Algebra

The model of d symplectic fermions constructed by Abe [1] gives an example of a C2cofinite vertex operator algebra admitting logarithmic modules. While the case d = 1 is a rigorous formulation of the well known triplet algebra, the case d > 1 has not yet been analyzed from the perspective of W-algebras. It is shown that in the latter case the W(2, 2 2−d−1, 3 2+d)-algebra is realized. With respe...

Lie-type higher derivations on operator algebras

 Motivated by the intensive and powerful works concerning additive‎ ‎mappings of operator algebras‎, ‎we mainly study Lie-type higher‎ ‎derivations on operator algebras in the current work‎. ‎It is shown‎ ‎that every Lie (triple-)higher derivation on some classical operator‎ ‎algebras is of standard form‎. ‎The definition of Lie $n$-higher‎ ‎derivations on operator algebras and related pot...

McKay’s E6 observation on the largest Fischer group

In this paper, we study McKay’s E6-observation on the largest Fischer 3-transposition group Fi24. We investigate a vertex operator algebra VF ♮ of central charge 2315 on which the Fischer group Fi24 naturally acts. We show that there is a natural correspondence between dihedral subgroups of Fi24 and certain vertex operator subalgebras constructed by the nodes of the affine E6 diagram by investi...

Integral forms in vertex operator algebras which are invariant under finite groups

For certain vertex operator algebras (e.g., lattice type) and given finite group of automorphisms, we prove existence of a positive definite integral form invariant under the group. Applications include an integral form in the Moonshine VOA which is invariant under the Monster, and examples in other lattice type VOAs.