Wreath Product Action on Generalized Boolean Algebras

Wreath Product Action on Generalized Boolean Algebras

Let G be a finite group acting on the finite set X such that the corresponding (complex) permutation representation is multiplicity free. There is a natural rank and order preserving action of the wreath product G ∼ Sn on the generalized Boolean algebra BX(n). We explicitly block diagonalize the commutant of this action.

Sequential Convergences on Generalized Boolean Algebras

In this paper we investigate convergence structures on a generalized Boolean algebra and their relations to convergence structures on abelian lattice ordered groups.

Generalized Join-hemimorphisms on Boolean Algebras

We introduce the notions of generalized join-hemimorphism and generalized Boolean relation as an extension of the notions of join-hemimorphism and Boolean relation, respectively. We prove a duality between these two notions.Wewill also define a generalization of the notion of Boolean algebra with operators by considering a finite family of Boolean algebras endowed with a generalized join-hemimo...

New applications of the wreath product of forest algebras

We give several new applications of the wreath product of forest algebras to the study of logics on trees. These include new simplified proofs of necessary conditions for definability in CTL and first-order logic with the ancestor relation; a sequence of identities satisfied by all forest languages definable in PDL; and new examples of languages outsideCTL, along with an application to the ques...

Continuum Cardinals Generalized to Boolean Algebras