An introduction to E*-unitary inverse semigroups - from an old fashioned perspective

Thity years ago, in 1972, H. E. Scheiblich published the first usable description of the free inverse semigoup 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 "Ïnverse 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 latter theory in the light of the earlier perspective that grew from Scheiblich's result.