Symmetries in synaptic algebras

被引：10

作者：

Foulis, David J. ^{[1
]}

Pulmannova, Sylvia ^{[2
]}

机构：

[1] Univ Massachusetts, Dept Math & Stat, Amherst, MA 01003 USA

[2] Slovak Acad Sci, Math Inst, SK-81473 Bratislava, Slovakia

来源：

MATHEMATICA SLOVACA | 2014年 / 64卷 / 03期

关键词：

synaptic algebra; Jordan algebra; order-unit space; projection; symmetry equivalence of projections; relative center property; LATTICE;

D O I：

10.2478/s12175-014-0238-2

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

A synaptic algebra is a generalization of the Jordan algebra of self-adjoint elements of a von Neumann algebra. We study symmetries in synaptic algebras, i.e., elements whose square is the unit element, and we investigate the equivalence relation on the projection lattice of the algebra induced by finite sequences of symmetries. In case the projection lattice is complete, or even centrally orthocomplete, this equivalence relation is shown to possess many of the properties of a dimension equivalence relation on an orthomodular lattice. (C) 2014 Mathematical Institute Slovak Academy of Sciences

引用

页码：751 / 776

页数：26