Gerald Höhn

Framed Vertex Operator Algebras, Codes and the Moonshine Module

Abstract:For a simple vertex operator algebra whose Virasoro element is a sum of commutative Virasoro elements of central charge ½, two codes are introduced and studied. It is proved that such vertex operator algebras are rational. For lattice vertex operator algebras and related ones, decompositions into direct sums of irreducible modules for the product of the Virasoro algebras of central charge ½ are explicitly described. As an application, the decomposition of the moonshine vertex operator algebra is obtained for a distinguished system of 48 Virasoro algebras.

The 290 fixed-point sublattices of the Leech lattice

Abstract We determine the orbits of fixed-point sublattices of the Leech lattice with respect to the action of the Conway group Co 0 . There are 290 such orbits. Detailed information about these lattices, the corresponding coinvariant lattices, and the stabilizing subgroups, is tabulated in several tables.

ON A THEOREM OF GARZA REGARDING ALGEBRAIC NUMBERS WITH REAL CONJUGATES

We give a new and simple proof of a theorem of Garza estimating the height (or Mahler measure) of an algebraic number with real conjugates.