ar X iv : m at h / 06 11 35 5 v 1 [ m at h . R T ] 1 3 N ov 2 00 6 Moonshine for Rudvalis ’ s sporadic group II ∗

ar X iv : m at h / 06 09 44 9 v 1 [ m at h . R T ] 1 5 Se p 20 06 Moonshine for Rudvalis ’ s sporadic group I ∗

We introduce the notion of vertex operator superalgebra with enhanced conformal structure, which is a refinement of the notion of vertex operator superalgebra. We exhibit several examples, including a particular one which is self-dual, and whose full symmetry group is a direct product of a cyclic group of order seven with the sporadic simple group of Rudvalis. We thus obtain an analogue of Mons...

ar X iv : m at h / 06 11 45 2 v 1 [ m at h . A G ] 1 5 N ov 2 00 6 UNIRATIONALITY OF CERTAIN SUPERSINGULAR K 3 SURFACES IN CHARACTERISTIC

We show that every supersingular K3 surface in characteristic 5 with Artin invariant ≤ 3 is unirational.

ar X iv : m at h / 06 11 38 6 v 1 [ m at h . R A ] 1 3 N ov 2 00 6 Quasi Q n - filiform Lie algebras ∗

In this paper we explicitly determine the derivation algebra, automorphism group of quasi Qn-filiform Lie algebras, and applying some properties of root vector decomposition we obtain their isomorphism theorem. AMS Classification: 17B05; 17B30

ar X iv : h ep - l at / 0 11 00 06 v 3 6 N ov 2 00 1 1 Matrix elements of ∆ S = 2 operators with Wilson fermions

ar X iv : m at h / 06 11 35 3 v 1 [ m at h . G N ] 1 2 N ov 2 00 6 SQUARES OF MENGER - BOUNDED GROUPS

Using a portion of the Continuum Hypothesis, we prove that there is a Menger-bounded (also called o-bounded) subgroup of the Baire group Z, whose square is not Menger-bounded. This settles a major open problem concerning boundedness notions for groups, and implies that Menger-bounded groups need not be Scheepers-bounded.