Topological structure of the unitary group of certain C*-algebras

被引：0

作者：

Visnescu, Bogdan ^{[1
,2
]}

机构：

[1] Univ N Florida, Dept Math & Stat, Jacksonville, FL 32224 USA

[2] Acad Romana, Inst Math Simion Stoilow, Bucharest 014700, Romania

来源：

JOURNAL OF OPERATOR THEORY | 2008年 / 60卷 / 01期

关键词：

C*-algebras; unitary group; homotopy groups;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let 0 - B (i)-> E (pi)-> A -> 0 be a short exact sequence of C*-algebras where A is a purely infinite simple C*-algebra and B is an essential ideal of E. In the case B is the compacts or a nonunital purely infinite simple C*-algebra we completely determine the homotopy groups of the unitary group of E in terms of K-theory. The result can be viewed as a generalization of the well-known Kuiper's theorem to a new class of C*-algebras (including certain separable C*-algebras).

引用

页码：113 / 124

页数：12

共 19 条

[11] K-THEORY AND MULTIPLIERS OF STABLE C-STAR-ALGEBRAS [J].

MINGO, JA .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1987, 299 (01) :397-411

[12]

RIEFFEL MA, 1987, J OPERAT THEOR, V17, P237

[13] ON THE HOMOTOPY TYPE OF THE REGULAR GROUP OF A REAL W-STAR - ALGEBRA [J].

SCHRODER, H .

INTEGRAL EQUATIONS AND OPERATOR THEORY, 1986, 9 (05) :694-705

[14]

Thomsen K., 1991, K-THEORY, V4, P245, DOI 10.1007/BF00569449

[15] DIAGONALIZING PROJECTIONS IN MULTIPLIER ALGEBRAS AND IN MATRICES OVER A C-STAR-ALGEBRA [J].

ZHANG, S .

PACIFIC JOURNAL OF MATHEMATICS, 1990, 145 (01) :181-200

[16] CERTAIN C-ASTERISK-ALGEBRAS WITH REAL RANK ZERO AND THEIR CORONA AND MULTIPLIER ALGEBRAS .1. [J].

ZHANG, S .

PACIFIC JOURNAL OF MATHEMATICS, 1992, 155 (01) :169-197

[17] On the homotopy type of the unitary group and the Grassmann space of purely infinite simple C*-algebras [J].

Zhang, S .

K-THEORY, 2001, 24 (03) :203-225

[18]

ZHANG S, 1991, J OPERAT THEOR, V26, P283

[19] K1-GROUPS, QUASIDIAGONALITY, AND INTERPOLATION BY MULTIPLIER PROJECTIONS [J].

ZHANG, SA .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1991, 325 (02) :793-818

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