Related papers: Lexicographic Product vs $\mathbb Q$-perfect and $…
We will study the existence of different types of the Riesz Decomposition Property for the lexicographic product of two partially ordered groups. A special attention will be paid to the lexicographic product of the group of the integers…
We study conditions when a certain type of the Riesz Decomposition Property (RDP for short) holds in the lexicographic product of two po-groups. Defining two important properties of po-groups, we extend known situations showing that the…
We establish conditions when a certain type of the Riesz Decomposition Property (RDP) holds in the lexicographic product of two po-groups. It is well known that the resulting product is an $\ell$-group if and only if the first one is…
Kite pseudo effect algebras were recently introduced as a class of interesting examples of pseudo effect algebras using a po-group, an index set and two bijections on the index set. We represent kite pseudo effect algebras with a special…
We define a new class of pseudo effect algebras, called kite pseudo effect algebras, which is connected with partially ordered groups not necessarily with strong unit. In such a case, starting even with an Abelian po-group, we can obtain a…
In the paper we investigate a class of effect algebras which can be represented in the form of the lexicographic product $\Gamma(H\lex G,(u,0))$, where $(H,u)$ is an Abelian unital po-group and $G$ is an Abelian directed po-group. We study…
We discuss the relationships between effect algebras with the Riesz Decomposition Property and partially ordered groups with interpolation. We show that any $\sigma$-orthocomplete atomic effect algebra with the Riesz Decomposition Property…
Recently in \cite{Dvu3} it was shown that if a pseudo effect algebra satisfies a kind of the Riesz Decomposition Property ((RDP) for short), then its state space is either empty or a nonempty simplex. This will allow us to prove a…
We define a new class of pseudo effect algebras, called kite pseudo effect algebras, which is connected not necessarily with partially ordered groups, but rather with generalized pseudo effect algebras where the greatest element is not…
We study $\mathbb H$-perfect pseudo MV-algebras, that is, algebras which can be split into a system of ordered slices indexed by the elements of an subgroup $\mathbb H$ of the group of the real numbers. We show when they can be represented…
We study algebraic conditions when a pseudo MV-algebra is an interval in the lexicographic product of an Abelian unital $\ell$-group and an $\ell$-group that is not necessary Abelian. We introduce $(H,u)$-perfect pseudo MV-algebras and…
For a perfect Lie algebra $\mathfrak{h}$ we classify all Lie algebras containing $\mathfrak{h}$ as a subalgebra of codimension $1$. The automorphism groups of such Lie algebras are fully determined as subgroups of the semidirect product…
The theory of direct decomposition of a centrally orthocomplete effect algebra into direct summands of various types utilizes the notion of a type-determining (TD) set. A pseudo-effect algebra (PEA) is a (possibly) noncommutative version of…
For an effect algebra $A$, we examine the category of all morphisms from finite Boolean algebras into $A$. This category can be described as a category of elements of a presheaf $R(A)$ on the category of finite Boolean algebras. We prove…
We quantize the Poisson-Lie group SL(2,R)^* as a bialgebra using the product of Kontsevich. The coproduct is a deformation of the coproduct that comes from the group structure. The resulting bialgebra structure is isomorphic to the quantum…
Recently a new family of pseudo effect algebras, called kite pseudo effect algebras, was introduced. Such an algebra starts with a po-group $G$, a set $I$ and with two bijections $\lambda,\rho:I \to I.$ Using a clever construction on the…
A lexicographic pseudo MV-algebra is an algebra that is isomorphic to an interval in the lexicographic product of a linear unital group with an arbitrary $\ell$-group. We present conditions when a pseudo MV-algebra is lexicographic. We show…
We consider a family of Hecke C*-algebras which can be realised as crossed products by semigroups of endomorphisms. We show by dilating representations of the semigroup crossed product that the category of representations of the Hecke…
If a graded Lie algebra is the direct sum of two graded sub Lie algebras, its bracket can be written in a form that mimics a "double sided semidirect product". It is called the {\it knit product} of the two subalgebras then. The integrated…
We study $\mathcal{O}$-operators and post-Lie products over the same Lie algebra compatible in a certain sense. We prove that the group product corresponding to the formal integration of the Lie algebra, which is adjacent to the sum of two…