Inverse Semigroups, The Theory Of Partial Symmetries

Symmetry is an organizing principle in the natural sciences. It has been usual in mathematics to identify the study of symmetry with the study of groups. It is a premise of this text, that there are aspects of symmetry which are represented by a generalization of groups called inverse semigroups.

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Symmetry is one of the most important organising principles in the natural sciences. The mathematical theory of symmetry has long been associated with group theory, but it is a basic premise of this book that there are aspects of symmetry which are more faithfully represented by a generalization of groups called inverse semigroups. The theory of inverse semigroups is described from its origins in the foundations of differential geometry through to its most recent applications in combinatorial group theory, and the theory tilings.