Description
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.
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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