Descripción del título
Introduction to Sofic and H...
This monograph presents some cornerstone results in the study of sofic and hyperlinear groups and the closely related Connes' embedding conjecture. These notions, as well as the proofs of many results, are presented in the framework of model theory for metric structures. This point of view, rarely explicitly adopted in the literature, clarifies the ideas therein, and provides additional tools to attack open problems. Sofic and hyperlinear groups are countable discrete groups that can be suitably approximated by finite symmetric groups and groups of unitary matrices. These deep and fruitful notions, introduced by Gromov and Radulescu, respectively, in the late 1990s, stimulated an impressive amount of research in the last 15 years, touching several seemingly distant areas of mathematics including geometric group theory, operator algebras, dynamical systems, graph theory, and quantum information theory. Several long-standing conjectures, still open for arbitrary groups, are now settled for sofic or hyperlinear groups. The presentation is self-contained and accessible to anyone with a graduate-level mathematical background. In particular, no specific knowledge of logic or model theory is required. The monograph also contains many exercises, to help familiarize the reader with the topics present
Monografía
monografia Rebiun17985577 https://catalogo.rebiun.org/rebiun/record/Rebiun17985577 151012s2015 deu| s |||| 0|eng d 9783319193335 978-3-319-19333-5 9783319193328 10.1007/978-3-319-19333-5. doi UPNA0462142 BUH Capraro, Valerio Introduction to Sofic and Hyperlinear Groups and Connes' Embedding Conjecture Recurso electrónico] by Valerio Capraro, Martino Lupini Servicio en línea Lecture Notes in Mathematics 2136 Introduction -- Sofic and hyperlinear groups -- Connes' embedding conjecture -- Conclusions Acceso restringido a miembros del Consorcio de Bibliotecas Universitarias de Andalucía This monograph presents some cornerstone results in the study of sofic and hyperlinear groups and the closely related Connes' embedding conjecture. These notions, as well as the proofs of many results, are presented in the framework of model theory for metric structures. This point of view, rarely explicitly adopted in the literature, clarifies the ideas therein, and provides additional tools to attack open problems. Sofic and hyperlinear groups are countable discrete groups that can be suitably approximated by finite symmetric groups and groups of unitary matrices. These deep and fruitful notions, introduced by Gromov and Radulescu, respectively, in the late 1990s, stimulated an impressive amount of research in the last 15 years, touching several seemingly distant areas of mathematics including geometric group theory, operator algebras, dynamical systems, graph theory, and quantum information theory. Several long-standing conjectures, still open for arbitrary groups, are now settled for sofic or hyperlinear groups. The presentation is self-contained and accessible to anyone with a graduate-level mathematical background. In particular, no specific knowledge of logic or model theory is required. The monograph also contains many exercises, to help familiarize the reader with the topics present Modo de acceso: world wide web Springer (e-Books) Mathematics Group theory Operator theory Mathematics Group Theory and Generalizations Operator Theory Lupini, Martino Lecture Notes in Mathematics (Servicio en línea) SpringerLink Books (Servicio en línea) Lecture Notes in Mathematics 2136