Research output: Contribution to Journal/Magazine › Journal article › peer-review
Research output: Contribution to Journal/Magazine › Journal article › peer-review
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TY - JOUR
T1 - Grothendieck group invariants for partly self-adjoint operator algebras.
AU - Power, Stephen C.
PY - 2000/2
Y1 - 2000/2
N2 - Partially ordered Grothendieck group invariants are introduced for general operator algebras and used in the classification of direct systems and direct limits of finite-dimensional complex incidence algebras with common reduced digraph H (systems of H-algebras). In particular the dimension distribution group G (A; C), defined for an operator algebra A and a self-adjoint subalgebra C, generalizes both the K0 group of a σ-unital C*-algebra B and the spectrum (fundamental relation) R(A) of a regular limit A of triangular digraph algebras. This invariant is more economical and computable than the regular Grothendieck group which nevertheless forms the basis for a complete classification of regular systems of H-algebras.
AB - Partially ordered Grothendieck group invariants are introduced for general operator algebras and used in the classification of direct systems and direct limits of finite-dimensional complex incidence algebras with common reduced digraph H (systems of H-algebras). In particular the dimension distribution group G (A; C), defined for an operator algebra A and a self-adjoint subalgebra C, generalizes both the K0 group of a σ-unital C*-algebra B and the spectrum (fundamental relation) R(A) of a regular limit A of triangular digraph algebras. This invariant is more economical and computable than the regular Grothendieck group which nevertheless forms the basis for a complete classification of regular systems of H-algebras.
U2 - 10.1142/S0129167X00000052
DO - 10.1142/S0129167X00000052
M3 - Journal article
VL - 11
SP - 41
EP - 64
JO - International Journal of Mathematics
JF - International Journal of Mathematics
SN - 0129-167X
IS - 1
ER -