The generalized Picard groups for finite dimensional C*-Hopf algebra coactions on unital C*-algebras

被引：0
作者：
Kodaka, Kazunori [1 ]
机构：
[1] Univ Ryukyus, Fac Sci, Dept Math Sci, Nishihara, Okinawa 9010213, Japan
来源：
TURKISH JOURNAL OF MATHEMATICS | 2019年 / 43卷 / 05期
关键词：
C*-algebra; C*-Hopf algebra; inclusion; Picard group; strong Morita equivalence; STRONG MORITA EQUIVALENCE; CROSSED-PRODUCTS; STABLE ISOMORPHISM; SATURATED ACTIONS; INCLUSIONS; BIMODULES;
D O I：
10.3906/mat-1905-37
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We shall generalize the notion of the strong Morita equivalence for coactions of a finite dimensional C*-Hopf algebra on a unital C*-algebra and define the Picard groups with respect to the generalized strong Morita equivalence. We call them the generalized Picard groups for coactions of a finite dimensional C*-Hopf algebra on a unital C*-algebra. We shall investigate basic properties of the generalized Picard groups and clarify the relation between the generalized Picard groups and the Picard groups for unital inclusions of unital C*-algebras.
引用
收藏
页码：2511 / 2539
页数：29
相关论文
共 50 条
[21]   JORDAN-HOLDER THEOREM FOR FINITE DIMENSIONAL HOPF ALGEBRAS [J].
Natale, Sonia .
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2015, 143 (12) :5195-5211
[22]   The homoclinic and heteroclinic C*-algebras of a generalized one-dimensional solenoid [J].
Thomsen, Klaus .
ERGODIC THEORY AND DYNAMICAL SYSTEMS, 2010, 30 :263-308
[23]   Cancellation for Inclusions of C*-algebras of Finite Depth [J].
Jeong, Ja A. ;
Osaka, Hiroyuki ;
Phillips, N. Christopher ;
Teruya, Tamotsu .
INDIANA UNIVERSITY MATHEMATICS JOURNAL, 2009, 58 (04) :1537-1564
[24]   HILBERT C*-BIMODULES OF FINITE INDEX AND APPROXIMATION PROPERTIES OF C*-ALGEBRAS [J].
Forough, Marzieh ;
Amini, Massoud .
GLASGOW MATHEMATICAL JOURNAL, 2018, 60 (02) :321-331
[25]   C*-PSEUDO-MULTIPLICATIVE UNITARIES, HOPF C*-BIMODULES AND THEIR FOURIER ALGEBRAS [J].
Timmermann, Thomas .
JOURNAL OF THE INSTITUTE OF MATHEMATICS OF JUSSIEU, 2012, 11 (01) :189-220
[26]   The C*-algebras of Compact Transformation Groups [J].
Archbold, Robert J. ;
Huef, Astrid An .
CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES, 2015, 67 (03) :481-506
[27]   The C*-algebra index for observable algebra in non-equilibrium Hopf spin models [J].
Wei, Xiaomin ;
Jiang, Lining .
ANNALS OF FUNCTIONAL ANALYSIS, 2022, 13 (04)
[28]   Tracial Cyclic Rokhlin Property for Automorphisms of Non-unital Simple C*-algebras [J].
Jamali, Saeid .
IRANIAN JOURNAL OF MATHEMATICAL SCIENCES AND INFORMATICS, 2024, 19 (01) :51-62
[29]   C*-ALGEBRAS ASSOCIATED TO HOMEOMORPHISMS TWISTED BY VECTOR BUNDLES OVER FINITE DIMENSIONAL SPACES [J].
Adamo, Maria Stella ;
Archey, Dawn E. ;
Forough, Marzieh ;
Georgescu, Magdalena C. ;
Jeong, J. A. A. ;
Strung, Karen R. ;
Viola, Maria Grazia .
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2024, 377 (03) :1597-1640
[30]   On Finite GK-Dimensional Nichols Algebras over Abelian Groups [J].
Andruskiewitsch, Nicolas ;
Angiono, Ivan ;
Heckenberger, Istvan .
MEMOIRS OF THE AMERICAN MATHEMATICAL SOCIETY, 2021, 271 (1329) :I-+
12345