Categories of Symmetries and Infinite-Dimensional Groups

This work contains the first explicit construction of hidden structures (mantles and trains). The author shows 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.
For mathematicians working in group theory, the study of the many infinite-dimensional groups has been carried out in an individual and non-coherent way. For the first time, these apparently disparate groups have been placed together, in order to construct the `big picture'. This book successfully gives an account of this - and shows how such seemingly dissimilar types such as the various groups of operators on Hilbert spaces, or current groups are shown to belong
to a bigger entitity. This is a ground-breaking text will be important reading for advanced undergraduate and graduate mathematicians.