AT-algebras and extensions of AT-algebras

被引：0

作者：

Yao, Hongliang ^{[1
,2
]}

机构：

[1] Nanjing Univ Sci & Technol, Sch Sci, Nanjing 210014, Peoples R China

[2] Tongji Univ, Dept Math, Shanghai 200092, Peoples R China

来源：

PROCEEDINGS OF THE INDIAN ACADEMY OF SCIENCES-MATHEMATICAL SCIENCES | 2010年 / 120卷 / 02期

关键词：

AF-algebra; AT-algebra; extension; index map; C-ASTERISK-ALGEBRAS; CLASSIFICATION; LIMITS;

D O I：

10.1007/s12044-010-0019-y

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Lin and Su classified AT-algebras of real rank zero. This class includes all AT-algebras of real rank zero as well as many C*-algebras which are not stably finite. An AT-algebra often becomes an extension of an AT-algebra by an AF-algebra. In this paper, we show that there is an essential extension of an AT-algebra by an AF-algebra which is not an AT-algebra. We describe a characterization of an extension E of an AT-algebra by an AF-algebra if E is an AT-algebra.

引用

页码：199 / 207

页数：9

共 7 条

[1] Extensions of C-*-algebras and quasidiagonality [J].

Brown, LG ;

Dadarlat, M .

JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES, 1996, 53 :582-600

[2]

Brown N. P., 2004, ADV STUD PURE MATH, V38, P19

[3] ON THE CLASSIFICATION OF C-ASTERISK-ALGEBRAS OF REAL RANK ZERO [J].

ELLIOTT, GA .

JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK, 1993, 443 :179-219

[4] EXTENSIONS OF INDUCTIVE LIMITS OF CIRCLE ALGEBRAS [J].

LIN, HX ;

RORDAM, M .

JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES, 1995, 51 :603-613

[5] Tracially quasidiagonal extensions [J].

Lin, HX .

CANADIAN MATHEMATICAL BULLETIN-BULLETIN CANADIEN DE MATHEMATIQUES, 2003, 46 (03) :388-399

[6] Classification of direct limits of generalized Toeplitz algebras [J].

Lin, HX ;

Su, HB .

PACIFIC JOURNAL OF MATHEMATICS, 1997, 181 (01) :89-140

[7]

YAO H, 2006, J E CHINA NORMAL U, V5, P1

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