Fountain and Gomes have shown that any proper left ample semigroup embeds into a so-calledW -product, which is a subsemigroup of a reversed semidirect product T ⋉ Y of a semilattice Y by a monoid T , where the action of T on Y is injective with images of the action being order ideals of Y. Proper left ample semigroups are proper left restriction, the latter forming a much wider class. The aim o...

We construct reflection functors on categories of modules over deformed wreath products of the preprojective algebra of a quiver. These functors give equivalences of categories associated to generic parameters which are in the same orbit under the Weyl group action. We give applications to the representation theory of symplectic reflection algebras of wreath product groups.

It is shown that membership in rational subsets of wreath products H ≀ V with H a finite group and V a virtually free group is decidable. On the other hand, it is shown that there exists a fixed finitely generated submonoid in the wreath product Z ≀ Z with an undecidable membership problem.

It is shown that membership in rational subsets of wreath products H ≀ V with H a finite group and V a virtually free group is decidable. On the other hand, it is shown that there exists a fixed finitely generated submonoid in the wreath product Z ≀ Z with an undecidable membership problem.