8 papers
Automorphism group schemes of lattice vertex algebras
Scott Carnahan, Hayate Kobayashi
Given a positive definite even lattice and a commutative ring, there is a standard construction of a lattice vertex algebra over the commutative ring, and it admits a natural gradi…
Why do the symmetries of the monster vertex algebra form a finite simple group?
Scott Carnahan
Together with their 1988 construction of the monster vertex algebra , Frenkel, Lepowsky, and Meurman showed that the largest sporadic simple group, known as the Fischer…
Monstrous Moonshine for integral group rings
Scott Carnahan, Satoru Urano
We propose a conjecture that is a substantial generalization of the genus zero assertions in both Monstrous Moonshine and Modular Moonshine. Our conjecture essentially asserts that…
Monstrous Moonshine over Z?
Scott Carnahan
Monstrous Moonshine was extended in two complementary directions during the 1980s and 1990s, giving rise to Norton's Generalized Moonshine conjecture and Ryba's Modular Moonshine c…
Characterizing Moonshine Functions by Vertex-Operator-Algebraic Conditions
Scott Carnahan, Takahiro Komuro, Satoru Urano
Given a holomorphic -cofinite vertex operator algebra with graded dimension , Borcherds's proof of the monstrous moonshine conjecture implies any finite order autom…
A Self-Dual Integral Form of the Moonshine Module
Scott Carnahan
We construct a self-dual integral form of the moonshine vertex operator algebra, and show that it has symmetries given by the Fischer-Griess monster simple group. The existence of…