Extensions of quasidiagonal $C^*$-algebras and controlling the $K_0$-map of embeddings

Iason Moutzouris

Extensions of quasidiagonal $C^*$-algebras and controlling the $K_0$-map of embeddings

Operator Algebras 2022-09-30 v3

Authors: Iason Moutzouris

Abstract

We study the validity of the Blackadar-Kirchberg conjecture for extensions of separable, nuclear, quasidiagonal $C^*$ -algebras that satisfy the UCT. More specifically, we show that the conjecture for the extension has an affirmative answer if the ideal lies in a class of $C^*$ -algebras that is closed under local approximations and contains all separable ASH algebras, as well as certain classes of simple, unital $C^*$ -algebras and crossed products of unital $C^*$ -algebras with the integers.

Keywords

quasidiagonal c*-algebras extensions blackadar-kirchberg conjecture uct ash algebras k0-map embeddings

Cite

@article{arxiv.2112.03224,
  title  = {Extensions of quasidiagonal $C^*$-algebras and controlling the $K_0$-map of embeddings},
  author = {Iason Moutzouris},
  journal= {arXiv preprint arXiv:2112.03224},
  year   = {2022}
}

Comments

36 pages, revision based on referree's comments. To appear in the Journal of Operator Theory

Extensions of quasidiagonal $C^*$-algebras and controlling the $K_0$-map of embeddings

Abstract

Keywords

Cite

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