Triangular UHF algebras over arbitrary fields

Author:
R. L. Baker

Journal:
Proc. Amer. Math. Soc. **123** (1995), 67-79

MSC:
Primary 46K50; Secondary 16S99

DOI:
https://doi.org/10.1090/S0002-9939-1995-1215025-4

MathSciNet review:
1215025

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Abstract | References | Similar Articles | Additional Information

Abstract: Let *K* be an arbitrary field. Let be a sequence of positive integers, and let there be given a family of unital *K*-monomorphisms such that whenever , where is the *K*-algebra of all upper triangular matrices over *K*. A *triangular UHF* (*TUHF*) *K-algebra* is any *K*-algebra that is *K*-isomorphic to an algebraic inductive limit of the form . The first result of the paper is that if the embeddings satisfy certain natural dimensionality conditions and if is an arbitrary TUHF *K*-algebra, then is *K*-isomorphic to , only if the supernatural number, , of is less than or equal to the supernatural number, , of . Thus, if the embeddings also satisfy the above dimensionality conditions, then is *K*-isomorphic to , only if . The second result of the paper is a nontrivial "triangular" version of the fact that if *p, q* are positive integers, then there exists a unital *K*-monomorphism , only if . The first result of the paper depends directly on the second result.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1995-1215025-4

Keywords:
Triangular UHF *K*-algebras,
*K*-algebras,
inductive limits

Article copyright:
© Copyright 1995
American Mathematical Society