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Introduction to Sofic and Hyperlinear groups and Connes' embedding conjecture by Capraro, Valerio; Lupini, Martino is a scholarly article available to read on EtoBox.

What is Introduction to Sofic and Hyperlinear groups and Connes' embedding conjecture about?

Sofic and hyperlinear groups are the countable discrete groups that can be approximated in a suitable sense by finite symmetric groups and groups of unitary matrices. These notions turned out to be very deep and fruitful, and stimulated in the last 15 years an impressive amount of research touching several seemingly distant areas of mathematics including geometric group theory, operator algebras, dynamical systems, graph theory, and more recently even quantum information theory. Several longstanding conjectures that are still open for arbitrary groups were settled in the case of sofic or hyperlinear groups. These achievements aroused the interest of an increasing number of researchers into some fundamental questions about the nature of these approximation properties. Many of such problems are to this day still open such as, outstandingly: Is there any countable discrete group that is not sofic or hyperlinear? A similar pattern can be found in the study of II_1 factors. In this case the famous conjecture due to Connes (commonly known as the Connes embedding conjecture) that any II_1 factor can be approximated in a suitable sense by matrix algebras inspired several breakthroughs in t

Author

Capraro, Valerio; Lupini, Martino

Published

2013

Language

EN