Approximately finite-dimensional C*-algebras

Karl Heinrich Hofmann; Francisco Javier Thayer

  • Publisher: Instytut Matematyczny Polskiej Akademi Nauk(Warszawa), 1980

Abstract

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CONTENTSIntroduction........................................................................................................................... 51. Finite-dimensional C*-algebras.................................................................................. 8 The objects...................................................................................................................... 8 The morphisms.............................................................................................................. 9 The matrix calculus........................................................................................................ 13 The graphic representation.......................................................................................... 16 Matrix units....................................................................................................................... 172. Almost finite-dimensional C*-algebras..................................................................... 18 The definitions................................................................................................................. 18 Examples......................................................................................................................... 22 Bratteli's scheme............................................................................................................ 23 The separable case....................................................................................................... 25 More examples................................................................................................................ 263. Ideals in AFC*-algebras................................................................................................ 284. Bratteli diagrams and partially ordered sets............................................................. 30 Augmented posets......................................................................................................... 30 Ideals of augmented posets........................................................................................ 32 The lattice of ideals of an augmented poset............................................................. 33 AFO-aJgebras and augmented posets have equivalent ideal theories............... 345. The spectral theory of augmented posets................................................................. 35 Filters and prime ideals................................................................................................ 35 Hull-kernel topologies................................................................................................... 37 AFC*-algebras and augmented posets have equivalent spectral theories........... 40 Prim A characterized for separable AFC*-algebraB................................................. 45 On the center of AFC*-algebras................................................................................... 46 The isomorphy of separable AFC*-algebras reflected in their augmented posets... 486. Problems.......................................................................................................................... 53Appendix. Some remarks on the distributivity of semilattices.................................... 54References........................................................................................................................... 58

How to cite

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Karl Heinrich Hofmann, and Francisco Javier Thayer. Approximately finite-dimensional C*-algebras. Warszawa: Instytut Matematyczny Polskiej Akademi Nauk, 1980. <http://eudml.org/doc/268488>.

@book{KarlHeinrichHofmann1980,
abstract = {CONTENTSIntroduction........................................................................................................................... 51. Finite-dimensional C*-algebras.................................................................................. 8 The objects...................................................................................................................... 8 The morphisms.............................................................................................................. 9 The matrix calculus........................................................................................................ 13 The graphic representation.......................................................................................... 16 Matrix units....................................................................................................................... 172. Almost finite-dimensional C*-algebras..................................................................... 18 The definitions................................................................................................................. 18 Examples......................................................................................................................... 22 Bratteli's scheme............................................................................................................ 23 The separable case....................................................................................................... 25 More examples................................................................................................................ 263. Ideals in AFC*-algebras................................................................................................ 284. Bratteli diagrams and partially ordered sets............................................................. 30 Augmented posets......................................................................................................... 30 Ideals of augmented posets........................................................................................ 32 The lattice of ideals of an augmented poset............................................................. 33 AFO-aJgebras and augmented posets have equivalent ideal theories............... 345. The spectral theory of augmented posets................................................................. 35 Filters and prime ideals................................................................................................ 35 Hull-kernel topologies................................................................................................... 37 AFC*-algebras and augmented posets have equivalent spectral theories........... 40 Prim A characterized for separable AFC*-algebraB................................................. 45 On the center of AFC*-algebras................................................................................... 46 The isomorphy of separable AFC*-algebras reflected in their augmented posets... 486. Problems.......................................................................................................................... 53Appendix. Some remarks on the distributivity of semilattices.................................... 54References........................................................................................................................... 58},
author = {Karl Heinrich Hofmann, Francisco Javier Thayer},
keywords = {primitive spectrum; separable approximately finite-dimensional C*- algebra; spectral space; space of prime ideals},
language = {eng},
location = {Warszawa},
publisher = {Instytut Matematyczny Polskiej Akademi Nauk},
title = {Approximately finite-dimensional C*-algebras},
url = {http://eudml.org/doc/268488},
year = {1980},
}

TY - BOOK
AU - Karl Heinrich Hofmann
AU - Francisco Javier Thayer
TI - Approximately finite-dimensional C*-algebras
PY - 1980
CY - Warszawa
PB - Instytut Matematyczny Polskiej Akademi Nauk
AB - CONTENTSIntroduction........................................................................................................................... 51. Finite-dimensional C*-algebras.................................................................................. 8 The objects...................................................................................................................... 8 The morphisms.............................................................................................................. 9 The matrix calculus........................................................................................................ 13 The graphic representation.......................................................................................... 16 Matrix units....................................................................................................................... 172. Almost finite-dimensional C*-algebras..................................................................... 18 The definitions................................................................................................................. 18 Examples......................................................................................................................... 22 Bratteli's scheme............................................................................................................ 23 The separable case....................................................................................................... 25 More examples................................................................................................................ 263. Ideals in AFC*-algebras................................................................................................ 284. Bratteli diagrams and partially ordered sets............................................................. 30 Augmented posets......................................................................................................... 30 Ideals of augmented posets........................................................................................ 32 The lattice of ideals of an augmented poset............................................................. 33 AFO-aJgebras and augmented posets have equivalent ideal theories............... 345. The spectral theory of augmented posets................................................................. 35 Filters and prime ideals................................................................................................ 35 Hull-kernel topologies................................................................................................... 37 AFC*-algebras and augmented posets have equivalent spectral theories........... 40 Prim A characterized for separable AFC*-algebraB................................................. 45 On the center of AFC*-algebras................................................................................... 46 The isomorphy of separable AFC*-algebras reflected in their augmented posets... 486. Problems.......................................................................................................................... 53Appendix. Some remarks on the distributivity of semilattices.................................... 54References........................................................................................................................... 58
LA - eng
KW - primitive spectrum; separable approximately finite-dimensional C*- algebra; spectral space; space of prime ideals
UR - http://eudml.org/doc/268488
ER -

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