McAlister's P-Theorem via Schützenberger Graphs

Abstract

We give a short proof, using Schützenberger graphs, of McAlister's P-theorem. The proof, when restricted to free inverse semigroups, turns into Munn's geometric multiplication of Munn trees.

Mathematics Subject Classification:

• 20M07

Acknowledgment

The author was supported in part by Praxis XXI scholarship BPD 16306 98, by NSF-NATO postdoctoral fellowship DGE-9972697, by the FCT and POCTI approved project POCTI/MAT/37670/2001 in participation with the European Community Fund FEDER; the author also received support from INTAS grant 99-1224.INTAS and from FCT through Centro de Matemática da Universidade do Porto. Much of this research took place at the Quasicrystals Workshop at the University of Essex in 1999 funded by EPSRC grant number GR/M6544.