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Grothendieck group invariants for partly self-adjoint operator algebras.

Research output: Contribution to journalJournal article


Journal publication date02/2000
JournalInternational Journal of Mathematics
Number of pages24
Original languageEnglish


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.