Amalgams of finite inverse semigroups

Amalgams of Free Inverse Semigroups

We study inverse semigroup amalgams of the form S U T where S and T are free inverse semigroups and U is an arbitrary nitely generated inverse subsemigroup of S and T. We make use of recent work of Bennett to show that the word problem is decidable for any such amalgam. This is in contrast to the general situation for semigroup amalgams, where recent work of Birget, Margolis and Meakin shows th...

A Note on Amalgams of Inverse Semigroups

Amalgams of inverse semigroups and reversible two-counter machines

We show that the word problem for an amalgam [S1, S2;U,ω1, ω2] of inverse semigroups may be undecidable even if we assume S1 and S2 (and therefore U) to have finite R-classes and ω1, ω2 to be computable functions, interrupting a series of positive decidability results on the subject. This is achieved by encoding into an appropriate amalgam of inverse semigroups 2-counter machines with sufficien...

Fast Fourier Transforms for Finite Inverse Semigroups

We extend the theory of fast Fourier transforms on finite groups to finite inverse semigroups. We use a general method for constructing the irreducible representations of a finite inverse semigroup to reduce the problem of computing its Fourier transform to the problems of computing Fourier transforms on its maximal subgroups and a fast zeta transform on its poset structure. We then exhibit exp...

Finite Presentability of HNN Extensions of Inverse Semigroups

HNN extensions of inverse semigroups, where the associated inverse subsemigroups are order ideals of the base, are defined by means of a construction based upon the isomorphism between the categories of inverse semigroups and inductive groupoids. The resulting HNN extension may conveniently be described by an inverse semigroup presentation, and we determine when an HNN extension with finitely g...