Limits of Finite Dimensional Nest Algebras

2000/06/22 by Alan Hopenwasser, Hopenwasser, Alan, Stephen C. Power +1
Mathematics · #47L35 (Secondary) #47L40 (Primary) #FOS: Mathematics #Operator Algebras (math.OA) #math.OA #msc:47L35 #msc:47L40

paper · pdf · doi:10.48550/arxiv.math/0006172

Approximately 37 pages. Minor revisions

arxiv created 2000/11/08 · arxiv updated 2009/11/30

Abstract

We introduce order conserving embeddings as a more general form of order preserving embeddings between finite dimensional nest algebras. The structure of these embeddings is determined, in terms of order indecomposable decompositions, and they are shown to be determined up to inner conjugacy by their induced maps on K₀. Classifications of direct systems and limit algebras are obtained in terms of dimension distribution groups.

Related

• Order Preservation in Limit Algebras
• Local characterisation of approximately finite operator algebras
• Finite rank operators in Lie ideals of nest algebras
• Infinite dimensional representations of finite dimensional algebras and amenability
• Join-completions of ordered algebras