| eBook ISBN: | 978-1-4704-2225-7 |
| Product Code: | MEMO/235/1107.E |
| List Price: | $80.00 |
| MAA Member Price: | $72.00 |
| AMS Member Price: | $48.00 |
| eBook ISBN: | 978-1-4704-2225-7 |
| Product Code: | MEMO/235/1107.E |
| List Price: | $80.00 |
| MAA Member Price: | $72.00 |
| AMS Member Price: | $48.00 |
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Book DetailsMemoirs of the American Mathematical SocietyVolume: 235; 2015; 109 pp
A unital separable \(C^\ast\)-algebra, \(A\) is said to be locally AH with no dimension growth if there is an integer \(d>0\) satisfying the following: for any \(\epsilon >0\) and any compact subset \({\mathcal F}\subset A,\) there is a unital \(C^\ast\)-subalgebra, \(B\) of \(A\) with the form \(PC(X, M_n)P\), where \(X\) is a compact metric space with covering dimension no more than \(d\) and \(P\in C(X, M_n)\) is a projection, such that \( \mathrm{dist}(a, B)<\epsilon \text{ for all } a\in\mathcal {F}.\)
The authors prove that the class of unital separable simple \(C^\ast\)-algebras which are locally AH with no dimension growth can be classified up to isomorphism by their Elliott invariant. As a consequence unital separable simple \(C^\ast\)-algebras which are locally AH with no dimension growth are isomorphic to a unital simple AH-algebra with no dimension growth.
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Table of Contents
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Chapters
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1. Introduction
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2. Preliminaries
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3. Definition of ${\mathcal C}_g$
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4. $C^*$-algebras in ${\mathcal C}_g$
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5. Regularity of $C^*$-algebras in ${\mathcal C}_1$
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6. Traces
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7. The unitary group
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8. ${\mathcal Z}$-stability
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9. General Existence Theorems
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10. The uniqueness statement and the existence theorem for Bott map
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11. The Basic Homotopy Lemma
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12. The proof of the uniqueness theorem 10.4
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13. The reduction
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14. Appendix
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A unital separable \(C^\ast\)-algebra, \(A\) is said to be locally AH with no dimension growth if there is an integer \(d>0\) satisfying the following: for any \(\epsilon >0\) and any compact subset \({\mathcal F}\subset A,\) there is a unital \(C^\ast\)-subalgebra, \(B\) of \(A\) with the form \(PC(X, M_n)P\), where \(X\) is a compact metric space with covering dimension no more than \(d\) and \(P\in C(X, M_n)\) is a projection, such that \( \mathrm{dist}(a, B)<\epsilon \text{ for all } a\in\mathcal {F}.\)
The authors prove that the class of unital separable simple \(C^\ast\)-algebras which are locally AH with no dimension growth can be classified up to isomorphism by their Elliott invariant. As a consequence unital separable simple \(C^\ast\)-algebras which are locally AH with no dimension growth are isomorphic to a unital simple AH-algebra with no dimension growth.
-
Chapters
-
1. Introduction
-
2. Preliminaries
-
3. Definition of ${\mathcal C}_g$
-
4. $C^*$-algebras in ${\mathcal C}_g$
-
5. Regularity of $C^*$-algebras in ${\mathcal C}_1$
-
6. Traces
-
7. The unitary group
-
8. ${\mathcal Z}$-stability
-
9. General Existence Theorems
-
10. The uniqueness statement and the existence theorem for Bott map
-
11. The Basic Homotopy Lemma
-
12. The proof of the uniqueness theorem 10.4
-
13. The reduction
-
14. Appendix
