Unital extensions of A F -algebras by purely infinite simple algebras

Junping Liu; Changguo Wei

Czechoslovak Mathematical Journal (2014)

  • Volume: 64, Issue: 4, page 989-1001
  • ISSN: 0011-4642

Abstract

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In this paper, we consider the classification of unital extensions of A F -algebras by their six-term exact sequences in K -theory. Using the classification theory of C * -algebras and the universal coefficient theorem for unital extensions, we give a complete characterization of isomorphisms between unital extensions of A F -algebras by stable Cuntz algebras. Moreover, we also prove a classification theorem for certain unital extensions of A F -algebras by stable purely infinite simple C * -algebras with nontrivial K 1 -groups up to isomorphism.

How to cite

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Liu, Junping, and Wei, Changguo. "Unital extensions of $AF$-algebras by purely infinite simple algebras." Czechoslovak Mathematical Journal 64.4 (2014): 989-1001. <http://eudml.org/doc/269832>.

@article{Liu2014,
abstract = {In this paper, we consider the classification of unital extensions of $AF$-algebras by their six-term exact sequences in $K$-theory. Using the classification theory of $C^*$-algebras and the universal coefficient theorem for unital extensions, we give a complete characterization of isomorphisms between unital extensions of $AF$-algebras by stable Cuntz algebras. Moreover, we also prove a classification theorem for certain unital extensions of $AF$-algebras by stable purely infinite simple $C^*$-algebras with nontrivial $K_1$-groups up to isomorphism.},
author = {Liu, Junping, Wei, Changguo},
journal = {Czechoslovak Mathematical Journal},
keywords = {$AF$-algebra; extension; purely infinite simple algebra; -algebra; extension; purely infinite simple algebra},
language = {eng},
number = {4},
pages = {989-1001},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Unital extensions of $AF$-algebras by purely infinite simple algebras},
url = {http://eudml.org/doc/269832},
volume = {64},
year = {2014},
}

TY - JOUR
AU - Liu, Junping
AU - Wei, Changguo
TI - Unital extensions of $AF$-algebras by purely infinite simple algebras
JO - Czechoslovak Mathematical Journal
PY - 2014
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 64
IS - 4
SP - 989
EP - 1001
AB - In this paper, we consider the classification of unital extensions of $AF$-algebras by their six-term exact sequences in $K$-theory. Using the classification theory of $C^*$-algebras and the universal coefficient theorem for unital extensions, we give a complete characterization of isomorphisms between unital extensions of $AF$-algebras by stable Cuntz algebras. Moreover, we also prove a classification theorem for certain unital extensions of $AF$-algebras by stable purely infinite simple $C^*$-algebras with nontrivial $K_1$-groups up to isomorphism.
LA - eng
KW - $AF$-algebra; extension; purely infinite simple algebra; -algebra; extension; purely infinite simple algebra
UR - http://eudml.org/doc/269832
ER -

References

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