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The Theory of Partial Symmetries

by Mark V Lawson (University of Wales, Bangor)

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.


  • Introduction to Inverse Semigroups
  • Extending Partial Symmetries
  • The Natural Partial Order
  • Ordered Groupoids
  • Extensions of Inverse Semigroups
  • Free Inverse Semigroups
  • E-unitary Inverse Semigroups
  • Enlargements
  • 0-E-unitary Inverse Semigroups
  • Category Actions and Inverse Semigroups

Readership: Mathematicians, and students of symmetry in the physical sciences.

Published by: World Scientific

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