Related papers: $E_0$-semigroups: around and beyond Arveson's work
The thesis is devoted to abstract, geometric and symmetric aspects of modern elementary particle theories. A new direction in constructing supersymmetric and superstring models based on consequent and strong consideration and inclusion of…
In this paper we study the main properties of the Ces\`aro means of bi-continuous semigroups, introduced and studied by K\"{u}hnemund in [24]. We also give some applications to Feller semigroups generated by second-order elliptic…
We introduce a general framework, based on \'etale topological categories, for studying discrete restriction semigroups and their algebras. Generalizing Paterson's universal groupoid of an inverse semigroup, we define the universal category…
We define tensor product decompositions of $E_0$-semigroups with a structure analogous to a classical theorem of Beurling. Such decompositions can be characterized by adaptedness and exactness of unitary cocycles. For CCR-flows we show that…
We introduce Poisson boundaries of II$_1$ factors with respect to density operators that give the traces. The Poisson boundary is a von Neumann algebra that contains the II$_1$ factor and is a particular example of the boundary of a unital…
In this paper we obtain some noncommutative multiplier theorems and maximal inequalities on semigroups. As applications, we obtain the corresponding individual ergodic theorems. Our main results extend some classical results of Stein and…
We prove that the Poisson boundary of a random walk with finite entropy on a non-elementary hyperbolic group can be identified with its hyperbolic boundary, without assuming any moment condition on the measure. We also extend our method to…
We study automaton structures, i.e. groups, monoids and semigroups generated by an automaton, which, in this context, means a deterministic finite-state letter-to-letter transducer. Instead of considering only complete automata, we…
We consider several classes of complete intersection numerical semigroups, aris- ing from many different contexts like algebraic geometry, commutative algebra, coding theory and factorization theory. In particular, we determine all the…
This expository article builds on lecture notes from a minicourse entitled "Cremona groups and CAT(0) cube complexes" and given by the author as part of the 2023 Riverside Workshop on Geometric Group Theory. It presents recent constructions…
The Poisson boundary of a finite direct product of affine automorphism groups of homogeneous trees is considered. The Poisson boundary is shown to be a product of ends of trees with a hitting measure for spread-out, aperiodic measures of…
In this work, we are concerned with the structure of sparse semigroups and some applications of them to Weierstrass points. We manage to describe, classify and find an upper bound for the genus of sparse semigroups. We also study the…
In this paper we define a new algebraic object: the disguised-groups. We show the main properties of the disguised-groups and, as a consequence, we will see that disguised-groups coincide with regular semigroups. We prove many of the…
In this paper we are interested to connect Koopman semigroups in Lebesgue funcion spaces $L^p(\R^+)$ and $C_0$-semigroups in Lebesgue sequence spaces $\ell^p$ for $1\le p < \infty$. To get this we use certain Poisson transformation ${\P}:…
We discuss the recent developments of semi-classical and micro-local analysis in the context of nilpotent Lie groups and for sub-elliptic operators. In particular, we give an overview of pseudo-differential calculi recently defined on…
Let $\Omega$ be an operator semigroup with generator $A$ in a sequentially complete locally convex topological vector space $E$. For a semigroup with generator $A+D$, where $D$ is a bounded linear operator on $E$, two integral equations are…
In this paper, we construct a new homology theory for semi-groups satisfying the self distributivity axiom or the idempotency axiom. Next, we consider the geometric realization corresponding to the homology theory. We continue with the…
We consider semigroups of transformations (partial mappings defined on a set $A$) closed under the set-theoretic intersection of mappings treated as subsets of $A\times A$. On such semigroups we define two relations: the relation of…
Recent algorithmic advances in algebraic automata theory drew attention to semigroupoids (semicategories). These are mathematical descriptions of typed computational processes, but they have not been studied systematically in the context of…
We introduce and develop the model-theoretic notions of absolute connectedness and type-absolute connectedness for groups. We prove that groups of rational points of split semisimple linear groups (that is, Chevalley groups) over arbitrary…