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 -