We prove that every closed exhaustive vector-valued modular measure on a lattice ordered effect algebra L can be decomposed into the sum of a Lyapunov exhaustive modular measure (i.e. its restriction to every interval of L has convex range) and an ”antiLyapunov” exhaustive modular measure. This result extends a Kluvanek-Knowles decomposition theorem for measures on Boolean algebras.

Let L be a supersolvable lattice with nonzero Möbius function. We show that the order complex of any rank-selected subposet of L admits a convex-ear decomposition. This proves many new inequalities for the h-vectors of such complexes, and shows that their g-vectors are M-

We encode arbitrary finite impartial combinatorial games in terms of lattice points in rational convex polyhedra. Encodings provided by these lattice games can be made particularly efficient for octal games, which we generalize to squarefree games. These additionally encompass all heap games in a natural setting, in which the Sprague–Grundy theorem for normal play manifests itself geometrically...

This Heisenberg group is a 2-step nilpotent Lie group and is important in the study of toroidal compactifications of Siegel moduli spaces. In fact, H (g,h) R is obtained as the unipotent radical of the parabolic subgroup of Sp(g+h,R) associated with the rational boundary component Fg ( cf. [F-C] p. 123 or [N] p. 21 ). For the motivation of the study of this Heisenberg group we refer to [Y4]-[Y8...

The normal subgroup theorem of Margulis expresses that many lattices in semi-simple Lie groups are simple up to finite error. In this talk, we give a short introduction to the normal subgroup theorem , including a brief review of the relevant notions about lattices, amenability, and property (T), as well as a short overview of the proof of the normal subgroup theorem. 1 Margulis's normal subgro...

The article is dedicated to groups in which the set of abnormal and normal subgroups (U -subgroups) forms a lattice. A complete description of these groups under the additional restriction that every counternormal subgroup is abnormal is obtained.