Examples of non-compact quantum group actions

被引：17

作者：

Soltan, Piotr Mikolaj ^{[1
,2
]}

机构：

[1] Univ Warsaw, Fac Phys, Dept Math Methods Phys, PL-00325 Warsaw, Poland

[2] Polish Acad Sci, Inst Math, PL-00901 Warsaw, Poland

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2010年 / 372卷 / 01期

关键词：

Quantum group; Quantum group action; C*-algebra; Quantum homogeneous space; MULTIPLICATIVE UNITARIES; ALGEBRAS; DUALITY; SU(2);

D O I：

10.1016/j.jmaa.2010.06.045

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We present two examples of actions of non-regular locally compact quantum groups on their homogeneous spaces. The homogeneous spaces are defined in a way specific to these examples, but the definitions we use have the advantage of being expressed in purely C*-algebraic language. We also discuss continuity of the obtained actions. Finally we describe in detail a general construction of quantum homogeneous spaces obtained as quotients by compact quantum subgroups. (C) 2010 Elsevier Inc. All rights reserved.

引用

页码：224 / 236

页数：13

共 30 条

[1] Non-semi-regular quantum groups coming from number theory [J].

Baaj, S ;

Skandalis, G ;

Vaes, S .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2003, 235 (01) :139-167

[2]

BAAJ S, 1992, CR ACAD SCI I-MATH, V314, P1021

[3]

BAAJ S, 1993, ANN SCI ECOLE NORM S, V26, P425

[4]

BOCA F, 1995, RECENT ADV OPERATOR, V232, P93

[5]

Echterhoff S, 2006, MEM AM MATH SOC, V180, P1

[6] A new characterisation of principal actions [J].

Ellwood, DA .

JOURNAL OF FUNCTIONAL ANALYSIS, 2000, 173 (01) :49-60

[7]

FISCHER R, 2003, THESIS U MUNSTER

[8] Rieffel deformation via crossed products [J].

Kasprzak, P. .

JOURNAL OF FUNCTIONAL ANALYSIS, 2009, 257 (05) :1288-1332

[9] Locally compact quantum groups [J].

Kustermans, J ;

Vaes, S .

ANNALES SCIENTIFIQUES DE L ECOLE NORMALE SUPERIEURE, 2000, 33 (06) :837-934

[10] Locally compact quantum groups in the universal setting [J].

Kustermans, J .

INTERNATIONAL JOURNAL OF MATHEMATICS, 2001, 12 (03) :289-338

← 1 2 3 →