Selbstduale Vertexoperatorsuperalgebren und das Babymonster (Self-dual Vertex Operator Super Algebras and the Baby Monster)
Gerald H\"ohn

TL;DR
This paper explores self-dual vertex operator superalgebras, constructs a new example related to the Baby Monster group, and introduces extremal VOAs and SVOAs, highlighting their existence at specific central charges and their analogies with lattices and codes.
Contribution
It constructs the shorter Moonshine module, a self-dual SVOA of central charge 23.5, and introduces the concept of extremal VOAs and SVOAs with existence results at various central charges.
Findings
Construction of the shorter Moonshine module for the Baby Monster
Existence of extremal VOAs at specific central charges
Existence of extremal SVOAs only at certain central charges
Abstract
We investigate self-dual vertex operator algebras (VOAs) and super algebras (SVOAs). Using the genus one correlation functions, it is shown that self-dual SVOAs exist only for half-integral central charges. It is described how self-dual SVOAs can be constructed from self-dual VOAs of larger central charge. The analogy with integral lattices and binary codes is emphasized. One main result is the construction of the shorter Moonshine module, a self-dual SVOA of central charge 23.5 on which the Baby monster - the second largest sporadic simple group - acts by automorphisms. The shorter Moonshine module has the character q^(-47/48)*(1+ 4371q^(3/2)+ 96256q^2+ 1143745q^(5/2) +...) and is the "shorter cousin" of the Moonshine module. Its lattice and code analog are the shorter Leech lattice and shorter Golay code. We conjecture that the shorter Moonshine module is the unique SVOA with this…
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Taxonomy
TopicsPeptidase Inhibition and Analysis · Algebraic structures and combinatorial models
