An introduction to E$^*$-untirary inverse semigroups - from an old fashioned perspective

by Donald McAlister

Thirty years ago, in 1972, H.E. Scheiblich published the first usable description of the free inverse semigroup on a set. This lead to a flowering of research on inverse semigroups, including the structure of E-unitary inverse semigroups. In a similar fashion, the publication of the book "Inverse semigroups: the theory of partial symmetry" by Mark V. Lawson, and, in particular, the chapters on applications of inverse semigroups to tilings have lead to another flowering of research; this time into the theory of E$^*$-unitary inverse semigroups. This talk will give an introduction to the later theory in the light of the earlier perspective that grew from Scheiblich's result.