Approximate Homotopy of Homomorphisms from C(x) Into a Simple C*-Algebra

By Huaxin Lin. 2006

53 citations recorded by the source corpus.

In this paper the author proves Generalized Homotopy Lemmas. These type of results play an important role in the classification theory of $*$-homomorphisms up to asymptotic unitary equivalence. Table of Contents: Prelude; The basic homotopy lemma for higher dimensional spaces; Purely infinite simple $C^*$-algebras; Approximate homotopy; Super homotopy; Postlude; Bibliography. (MEMO/205/963)

Subfields: Algebra and Number Theory, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/c0e266b44d9c3f6decd5305836a2478ead69d7bc

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In Algebra and Number Theory

1. Z. Niu
2. G. Gong
3. Huaxin Lin
4. W. Winter
5. N. Christopher Phillips
6. Andrew S. Toms
7. G. Elliott
8. David Kerr

In Mathematical Physics

1. Z. Niu
2. G. Gong
3. Huaxin Lin
4. W. Winter
5. Andrew S. Toms
6. N. Christopher Phillips
7. G. Elliott
8. David Kerr

Citations in the corpus

• A classification of finite simple amenable ${\cal Z}$-stable $C^*$-algebras, I: $C^*$-algebras with generalized tracial rank one. (2018, background): “4 of [65], for some large P, if (ε,F ,P) (with sufficiently small ε, and sufficiently large F) is a KL-triple for A, then [L] defines an element in KL(A,B) = KK(A,B).”
• Classification of finite simple amenable ${\cal Z}$-stable $C^*$-algebras (2014, background): “8 of [60] ) Let A be a unital amenable separable C∗-algebra.”
• A classification of finite simple amenable Z-stable C*-algebras, II, --C*-algebras with rational generalized tracial rank one (2019, unknown): “8 of [38], there is a δ1/2-G1-multiplicative contractive completely positive linear map L : C ⊗ C(T) → A such that ‖L(f ⊗ 1)− h(f)‖ < δ1/2 for all f ∈ G′ 1 and (e 26.”