Power, Stephen C. (2000) *Grothendieck group invariants for partly self-adjoint operator algebras.* International Journal of Mathematics, 11 (1). pp. 41-64. ISSN 0129-167X

## Abstract

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.

Item Type: | Article |
---|---|

Journal or Publication Title: | International Journal of Mathematics |

Subjects: | Q Science > QA Mathematics |

Departments: | Faculty of Science and Technology > Mathematics and Statistics |

ID Code: | 19365 |

Deposited By: | ep_ss_importer |

Deposited On: | 17 Nov 2008 16:45 |

Refereed?: | Yes |

Published?: | Published |

Last Modified: | 18 Aug 2017 01:12 |

Identification Number: | |

URI: | http://eprints.lancs.ac.uk/id/eprint/19365 |

### Actions (login required)

View Item |