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

Full-text PDF Free Access

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.

**[AAR]**D. J. Alkers, G. L. Alexanderson, asnd C. Reid,*More mathematical people*, Harcourt Brace Jovanovich, 1990. MR**1143310 (93b:01045)****[B1]**R. Baker,*Triangular UHF algebras*, J. Funct. Anal.**91**(1990), 182-212. MR**1054118 (91d:46056)****[B2]**-,*On certain Banach limits of triangular matrix algebras*, Houston J. Math. (to appear). MR**1688831 (2000m:46104)****[BL]**T. S. Blyth,*Module theory*, Oxford Univ. Press, London, 1990. MR**1070710 (91i:16001)****[PPW]**J. R. Peters, Y. T. Poon, and B. H. Wagner,*Triangular AF algebras*, Proc. J. Operator Theory**23**(1990), 81-114. MR**1054818 (91h:46102)****[P1]**S. C. Power,*Classifications of tensor products of triangular matrix algebras*, Proc. London Math. Soc. (3)**61**(1990), 571-614. MR**1069516 (92a:47053)****[P2]**-,*The classification of triangular subalgebras of*-*algebras*, Bull London Math. Soc.**22**(1990), 264-272.

Retrieve articles in *Proceedings of the American Mathematical Society*
with MSC:
46K50,
16S99

Retrieve articles in all journals with MSC: 46K50, 16S99

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