Topological Groupoid Quantales

被引：5
|
作者：
Palmigiano, A. [1 ]
Re, R. [2 ]
机构：
[1] Univ Amsterdam, Inst Log Language & Computat, NL-1090 GE Amsterdam, Netherlands
[2] Univ Catania, Dipartimento Matemat & Informat, I-95125 Catania, Italy
来源：
STUDIA LOGICA | 2010年 / 95卷 / 1-2期
关键词：
unital involutive quantale; regular frame; topological groupoid; etale groupoid; representation theorem; Penrose tilings;
D O I：
10.1007/s11225-010-9251-9
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We associate a canonical unital involutive quantale to a topological groupoid. When the groupoid is also etale, this association is compatible with but independent from the theory of localic etale groupoids and their quantales [9] of P. Resende. As a motivating example, we describe the connection between the quantale and the C*-algebra that both classify Penrose tilings, which was left as an open problem in [5].
引用
收藏
页码：125 / 137
页数：13
相关论文
共 50 条
  • [1] Topological Groupoid Quantales
    A. Palmigiano
    R. Re
    Studia Logica, 2010, 95 : 125 - 137
  • [2] Relational Representation of Groupoid Quantales
    Palmigiano, Alessandra
    Re, Riccardo
    ORDER-A JOURNAL ON THE THEORY OF ORDERED SETS AND ITS APPLICATIONS, 2013, 30 (01): : 65 - 83
  • [3] Relational Representation of Groupoid Quantales
    Alessandra Palmigiano
    Riccardo Re
    Order, 2013, 30 : 65 - 83
  • [4] Functoriality of groupoid quantales. I
    Resende, Pedro
    JOURNAL OF PURE AND APPLIED ALGEBRA, 2015, 219 (08) : 3089 - 3109
  • [5] Functoriality of Groupoid Quantales. II
    Juan Pablo Quijano
    Pedro Resende
    Applied Categorical Structures, 2021, 29 : 629 - 670
  • [6] Groupoid quantales: A non-etale setting
    Palmigiano, Alessandra
    Re, Riccardo
    JOURNAL OF PURE AND APPLIED ALGEBRA, 2011, 215 (08) : 1945 - 1957
  • [7] FUNDAMENTAL GROUPOID AS A TOPOLOGICAL GROUPOID
    BROWN, R
    DANESHNARUIE, G
    PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY, 1975, 19 (MAR) : 237 - 244
  • [8] Topological aspect of monodromy groupoid for a topological internal groupoid
    Akiz, H. Fulya
    Mucuk, Osman
    THIRD INTERNATIONAL CONFERENCE OF MATHEMATICAL SCIENCES (ICMS 2019), 2019, 2183
  • [9] THE HOLONOMY GROUPOID OF A LOCALLY TOPOLOGICAL GROUPOID
    AOF, MAESAF
    BROWN, R
    TOPOLOGY AND ITS APPLICATIONS, 1992, 47 (02) : 97 - 113
  • [10] The fundamental groupoid as a topological groupoid: Lasso topology
    Pakdaman, Ali
    Shahini, Freshte
    TOPOLOGY AND ITS APPLICATIONS, 2021, 302
12345