1994/03/01 by Alan Hopenwasser, Hopenwasser, Alan, Allan P. Donsig +2
Mathematics · #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Dynamical Systems (math.DS) #FOS: Mathematics #Functional Analysis (math.FA) #Operator Algebras (math.OA) #funct-an #math.DS #math.OA
paper · pdf · doi:10.48550/arxiv.funct-an/9403001
43 pages, AMS-TEX v2.1
arxiv created 1994/03/01 · openalex publication_date 1994/03/01 · arxiv updated 2016/08/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The matrix units of a digraph algebra, A, induce a relation, known as the diagonal order, on the projections in a masa in the algebra. Normalizing partial isometries in A act on these projections by conjugation; they are said to be order preserving when they respect the diagonal order. Order preserving embeddings, in turn, are those embeddings which carry order preserving normalizers to order preserving normalizers. This paper studies operator algebras which are direct limits of finite dimensional algebras with order preserving embeddings. We give a complete classification of direct limits of full triangular matrix algebras with order preserving embeddings. We also investigate the problem of characterizing algebras with order preserving embeddings.