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Grothendieck group invariants for partly self-adjoint operator algebras

S. C. Power
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Abstract

Various partially ordered Grothendieck group invariants are introduced for general operator algebras and these are 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, generalises both the K0 group of a sigma 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 so called regular Grothendieck group which nevertheless forms the basis for a complete classification of regular systems of H-algebras.

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S. C. Power. 1999-01-22. Grothendieck group invariants for partly self-adjoint operator algebras. https://arxiv.org/abs/math/9810051

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