Subdirectly irreducible \mathcal{RGC} -commutative right H-semigroups

A semigroup S is said to be ℛ-commutative if, for all elements a,b∈S, there is an element x∈S ¹ such that ab=bax. A semigroup S is called a generalized conditionally commutative (briefly, -commutative) semigroup if it satisfies the identity aba ²=a ² ba. An ℛ-commutative and -commutative semigroup is called an -commutative semigroup. A semigroup S is said to be a right H-semigroup if every right congruence of S is a congruence of S. In this paper we characterize the subdirectly irreducible semigroups in the class of -commutative right H-semigroups. Research supported by the Hungarian NFSR grant No T029525.     

On the Continuity of Inversion in Countably Compact Inverse Topological Semigroups

Let S be a countably compact Hausdorff space endowed with a continuous semigroup operation turning S into an inverse semigroup. It is shown that the inversion inv : x x^-1 in S is continuous provided one of the following conditions is satisfied: (1) the space S is sequential, (2) the semigroup S is Clifford, inversely regular, and topologically periodic, (3) the semigroup S is Clifford, topologically periodic and the square S × S is regular and countably compact. These results are close to the best possible since there is an example of a quasi-regular sequentially compact commutative inverse topological semigroup with discontinuous inversion.     

Some remarks on the inverse semigroup associated to the Cuntz-Li algebras

In this article, we prove that the inverse semigroup associated to the Cuntz-Li relations is strongly 0-E unitary and is an F ^?-inverse semigroup. We also identify the universal group of the inverse semigroup. This gives a conceptual explanation for the result obtained in S. Sundar (arXiv:1201.4620v1, 2012).     

Pseudo-amenability of certain semigroup algebras

In this paper, we investigate the pseudo-amenability of semigroup algebra ? ¹(S), where S is an inverse semigroup with uniformly locally finite idempotent set. In particular, we show that for a Brandt semigroup \(S={\mathcal{M}}^{0}(G,I)\), the pseudo-amenability of ? ¹(S) is equivalent to the amenability of G.     

Normed Groups and Their Applications in Noncommutative Differential Geometry

A normed semigroup is a semigroup having both rich topological and rich algebraic structure. This work is devoted to an abstract study of normed semigroups that arise in some problems of noncommutative geometry. The most interesting example, namely, the Abel semigroup , where A is a von Neumann algebra, is considered in detail. The definition of the latter semigroup is based on the notion of stable equivalence of normal elements of W^*-algebras, which generalizes the notion of stable equivalence of projectors. Bibliography: 8 titles.     

Measure Perturbations of Markovian Semigroups

The perturbation of the semigroup of a Borel right process by a class of signed measures on the state space of the process is studied. The perturbation is defined by a Feynman–Kac functional associated with the measure. Under appropriate conditions the perturbed semigroup is strongly continuous in L^p(m), 1 p< where m is a fixed excessive measure. Both existence and uniqueness of the associated Schrödinger type equation are investigated.     

Tight representations of semilattices and inverse semigroups

By a Boolean inverse semigroup we mean an inverse semigroup whose semilattice of idempotents is a Boolean algebra. We study representations of a given inverse semigroup in a Boolean inverse semigroup which are tight in a certain well defined technical sense. These representations are supposed to preserve as much as possible any trace of Booleanness present in the semilattice of idempotents of  . After observing that the Vagner–Preston representation is not tight, we exhibit a canonical tight representation for any inverse semigroup with zero, called the regular tight representation. We then tackle the question as to whether this representation is faithful, but it turns out that the answer is often negative. The lack of faithfulness is however completely understood as long as we restrict to continuous inverse semigroups, a class generalizing the E ^*-unitaries. Partially supported by CNPq.     

Ideals and Representations of Certain Semigroup Algebras

We characterize various types of ideals in ¹-Munn algebras with a bounded approximate identity, in terms of the ideals of their underlying algebras. Moreover, we show the correspondence between different types of *-representations of ¹-Munn algebras and *-representations of their underlying algebras. In the context of semigroup algebras, .rst we prove the conjecture which was proposed in [8]. Then we apply the results of the first part to build various representations of unital semigroup algebras of completely 0-simple inverse semigroups. This generalizes some of the Barnes results [1] with different and much shorter proofs.     

Polynomial functions over commutative semi-groups

Let S be a commutative semigroup. We consider the semigroup P(S) with respect to composition of all transformations p: S S of the form x a,x xⁿ or x axⁿ (a S; n N) and the semigroup P(S) containing only elements of the last two forms. Since all polynomials over S have the form a, xⁿ or ax these transformations are the so-called polynomial functions over S. We investigate the relationship between the structures of S and (S) resp. P(S) — a criterion on the commutativity of S has been shown by means of polynomial functions in 2.     

On <Emphasis Type="Italic">n</Emphasis>-Central Semigroups

A semigroup S is said to be n-central if xⁿ belongs to the center of S for every x S. We prove that every n-central semigroup is a semilattice of archimedean n-central semigroups. We obtain characterizations of simple (0-simple) n-central semigroups and describe subdirectly irreducible n-central semigroups. We also deal with the connection of n-central semigroups and E-k semigroups.     

Analyticity of the semigroup associated with the fluid-rigid body problem and local existence of strong solutions

In this paper, we study the linear operator associated with the fluid-rigid body problem. The operator was first introduced by T. Takahashi and M. Tucsnak (2004) [22]. For the general three-dimensional case, we prove that the corresponding semigroup is analytic on (p?2). In particular, when the solid is a ball in R³, the corresponding semigroup is analytic on L²(R³)∩Lp(R³)(p?6). And for this case, a unique local strong solution to the fluid-rigid body problem is derived.     

The inverse hull of the free semigroup on a set X

In this paper the inverse hull of the free semigroup on a non-empty set X is characterized. It is shown that if F^O is a certain semilattice and (G,*) is the free group on X, then is isomorphic to a Rees factor semigroup of a subsemigroup of (F^O x G, #), where (A,w)#(B,u) = ((A*w B)*w^–1, w*u). Several properties of , including Green's relations on are also determined.     

Conditions for Admissibility of Observation Operators and Boundedness of Hankel Operators

We derive new necessary and sufficient conditions for admissibility of observation operators for certain C ₀-semigroups. We also prove a new sufficient criterion for admissibility for observation operators with infinite-dimensional output space on contraction semigroups. If the contraction semigroup is completely non-unitary and its co-generator has finite defect indices, then this criterion is also necessary. In the case of the right shift semigroup on L ²(0,), these conditions translate into conditions for the boundedness of Hankel operators.     

The existence of global attractors for the norm-to-weak continuous semigroup and application to the nonlinear reaction-diffusion equations

In this paper, first, we introduce a new concept, called the norm-to-weak continuous semigroup in a Banach space, and give a technical theorem to verify this notion of continuity. Then we establish a general method which is necessary and sufficient to obtain the existence of the global attractor for this kind of semigroup. As an application, we obtain the existence of the global attractor for a nonlinear reaction-diffusion equation with a polynomial growth nonlinearity of arbitrary order and with some weak derivatives in the inhomogeneous term, the global attractors are obtained in L^p(Ω), and , respectively. A new a priori estimate method, called asymptotic a priori estimate, has been introduced. Since the solutions of the equation has no higher regularity and the semigroup associated the solutions is not continuous in L^p(Ω), and , the results in this part are new and appear to be optimal.     

Ebene algebraische Kurven vom Typ p,q

Let p,q be relatively prime integers with 2pr ^p,q be the numerical semigroup generated by p,q,{(p–1) (q–1)–1–(ip+jq)¦i+jr–2}. Then there exists a smooth projective curve X and a point x on X, such that H _r ^p,q is the set of orders of poles of the rational functions on X, which are regular on X\{x}; in other words: H _r ^p,q is a Weierstraß semigroup.     

The Linear Part of a Discontinuously Acting Euclidean Semigroup

Let ⁿ be a Euclidean space and let S be a Euclidean semigroup, i.e., a subsemigroup of the group of isometries of ⁿ. We say that a semigroup S acts discontinuously on ⁿ if the subset {s  S:sK ∩ K ≠ } is finite for any compact set K of ⁿ. The main results of this work areTheorem.If S is a Euclidean semigroup which acts discontinuously on ⁿ, then the connected component of the closure of the linear part ℓ(S) of S is a reducible group.Corollary.Let S be a Euclidean semigroup acting discontinuously on ⁿ; then the linear part ℓ(S) of S is not dense in the orthogonal group O(n).These results are the first step in the proof of the followingMargulis' Conjecture.If S is a crystallographic Euclidean semigroup, then S is a group.     

Cauchy Problem with Subcritical Nonlinearity

The semilinear parabolic system onRⁿwith subcritical nonlinearity is studied as an abstract evolutionary equation in a Banach spaceX ? ^p(Rⁿ). As in the case of bounded domains the existence of a strongly continuous semigroup of globalX^α-solutions and its dissipativeness is shown to follow from a single estimate of solutions. Despite the lack of compactness of the Sobolev embeddings inRⁿthe compactness of trajectories of the semigroup is proved using the auxiliary estimate of solutions in a weighted space ^p(Rⁿ, (1 + |x|²)^ν), and the existence of a global attractor is also shown. Thus this paper generalizes earlier considerations and provides a basis for further applications.     

A novel dual approach to nonlinear semigroups of Lipschitz operators

Lipschitzian semigroup refers to a one-parameter semigroup of Lipschitz operators that is strongly continuous in the parameter. It contains -semigroup, nonlinear semigroup of contractions and uniformly -Lipschitzian semigroup as special cases. In this paper, through developing a series of Lipschitz dual notions, we establish an analysis approach to Lipschitzian semigroup. It is mainly proved that a (nonlinear) Lipschitzian semigroup can be isometrically embedded into a certain -semigroup. As application results, two representation formulas of Lipschitzian semigroup are established, and many asymptotic properties of -semigroup are generalized to Lipschitzian semigroup.

     

Semistable measures and limit theorems on real andp-adic groups

For any locally compact groupG, we show that any locally tight homomorphism from a real directed semigroup intoM ¹ (G) (semigroup of probability measures onG) has a shift which extends to a continuous one-parameter semigroup. IfG is ap-adic algebraic group then the above holds even iff is not locally tight. These results are applied to give sufficient conditions for embeddability of some translate of limits of sequences of the form {v _n ^kn } and M ¹ (G) such that ()= ^M , for somek>1 and AutG (cf. Theorems 2.1, 2.4, 3.7).