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Endomorphisms of Z-absorbing C*-algebras without conditional expectations

Yasuhiko Sato

Abstract

We construct an endomorphism of the Jiang-Su algebra $\mathcal{Z}$ which does not admit a conditional expectation. This answers a question in the testamentary homework by E. Kirchberg. As an application, it is shown that any unital separable nuclear $\mathcal{Z}$-absorbing C*-algebra is non-transportable in the Cuntz algebra $\mathcal{O}_2$.

Endomorphisms of Z-absorbing C*-algebras without conditional expectations

Abstract

We construct an endomorphism of the Jiang-Su algebra which does not admit a conditional expectation. This answers a question in the testamentary homework by E. Kirchberg. As an application, it is shown that any unital separable nuclear -absorbing C*-algebra is non-transportable in the Cuntz algebra .
Paper Structure (4 sections, 7 theorems, 38 equations)

This paper contains 4 sections, 7 theorems, 38 equations.

Table of Contents

  1. Introduction
  2. Jiang and Su's connecting maps reconstructed
  3. Expectationless embeddings
  4. Non-transportable $\mathrm{C}^*$-al-ge-bra s

Key Result

Theorem 1.1

Theorems & Definitions (16)

  • Theorem 1.1
  • Definition 2.1
  • Proposition 2.2
  • proof
  • Lemma 3.1
  • proof
  • Proposition 3.2
  • proof
  • proof : Proof of Theorem 1.1
  • Corollary 3.3
  • ...and 6 more