1986/06/01 by K. R. Goodearl, David Handelman · 34 citations
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Advanced Operator Algebra Research #Mathematics #Tensor product #Hausdorff space #Separable space #Unit (ring theory) #Section (typography) #Second-countable space #Pure mathematics #Tensor product of algebras #Group (periodic table) #Tensor product of Hilbert spaces #Group algebra #Tensor (intrinsic definition) #Countable set #Ring (chemistry) #Locally compact space #Combinatorics #Algebra over a field #Tensor contraction #Mathematical analysis
paper · pdf · doi:10.4153/cjm-1986-032-0
published in Canadian Journal of Mathematics 38(3), 633-658 (Cambridge University Press)
openalex publication_date 1986/06/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04
We study direct limits of finite products of matrix algebras (i.e., locally matricial algebras), their ordered Grothendieck groups ( K 0 ), and their tensor products. Given a dimension group G , a general problem is to determine whether G arises as K 0 of a unit-regular ring or even as K 0 of a locally matricial algebra. If G is countable, this is well known to be true. Here we provide positive answers in case (a) the cardinality of G is ℵ 1 , or (b) G is an arbitrary infinite tensor product of the groups considered in (a), or (c) G is the group of all continuous real-valued functions on an arbitrary compact Hausdorff space. In cases (a) and (b), we show that G in fact appears as K 0 of a locally matricial algebra. Result (a) is the basis for an example due to de la Harpe and Skandalis of the failure of a determinantal property in a non-separable AF C *-algebra [ 18 , Section 3].