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Categories of Symmetries and Infinite-Dimensional Groups London Mathematical Society Monographs New Series



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This article summarizes work on symmetries and infinite-dimensional groups by Neretin and others. Neretin shows that many infinite-dimensional groups are only a small part of a much larger object, analogous to the way real numbers are embedded within complex numbers.
Key Features
Neretin shows that many infinite-dimensional groups are only a small part of a much larger object, analogous to the way real numbers are embedded within complex numbers.
This larger object is called a symmetry group, and it contains all of the infinite-dimensional groups.
Neretin and others have found many symmetry groups, including the Symmetric Group of order 8, the symmetry group of the square root of two, and the symmetry group of the Klein bottle.
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Features
Author Yu A. Neretin
ISBN 9780198511861
Publication Date 05/08/2007
Publisher Oxford University Press
Manufacturer Oxford University Press
Description

There are many types of infinite-dimensional groups, most of which have been studied separately from each other since the 1950's. It is now possible to fit these apparently disparate groups into one coherent picture. With the first explicit construction of hidden structures (mantles and trains), Neretin is able to show how many infinite-dimensional groups are in fact only a small part of a much larger object, analogous to the way real numbers are embedded within complex numbers.


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