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On the Stable Rank of Algebras of Operator Fields Over an N ‐Cube
Author(s) -
Ng Ping Wong,
Sudo Takahiro
Publication year - 2004
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/s0024609303002881
Subject(s) - mathematics , rank (graph theory) , cube (algebra) , bounded function , unital , base (topology) , operator (biology) , mathematics subject classification , operator algebra , combinatorics , pure mathematics , algebra over a field , mathematical analysis , chemistry , transcription factor , biochemistry , repressor , gene
Let A be a unital maximal full algebra of operator fields with base space [0, 1] k and fibre algebras{ A t } t ∈ [ 0 , 1 ] k . It is shown in this paper that the stable rank of A is bounded above by the quantitysup t ∈[ 0 , 1 ] ksr ( C ([ 0 , 1 ] k ) ⊗ A t ) , where ‘sr’ means stable rank. Using the above estimate, the stable ranks of the C*‐algebras of the (possibly higher rank) discrete Heisenberg groups are computed. 2000 Mathematics Subject Classification 47L99.