Related papers: Tannakian categories with semigroup actions

In this chapter we present transformation semigroups and their applications. We begin with Klein's approach to geometry based on invariants of transformation groups. Then we present symmetry groups in chemistry and in classical mechanics.…

In this paper we continue the study of groups of trace class and consider in particular the case of semi-direct products. One of the highlights is the theorem saying that the semi-direct product of a semisimple Lie group G and its Lie…

Using a variant of Schreier's Theorem, and the theory of Green's relations, we show how to reduce the computation of an arbitrary subsemigroup of a finite regular semigroup to that of certain associated subgroups. Examples of semigroups to…

The classical Juzvinski\u{i} Addition Theorem states that the entropy of an automorphism of a compact group decomposes along invariant subgroups. Thomas generalized the theorem to a skew-product setting. Using L. Bowen's f-invariant we…

We prove a boundedness criterion for a class of dyadic multilinear forms acting on two-dimensional functions. Their structure is more general than the one of classical multilinear Calder\'{o}n-Zygmund operators as several functions can now…

We consider actions of a group or a semigroup on a set, which generalize the setup of discrete logarithm based cryptosystems. Such cryptographic group actions have gained increasing attention recently in the context of isogeny-based…

The most developed aspect of the theory of finite semigroups is their classification in pseudovarieties. The main motivation for investigating such entities comes from their connection with the classification of regular languages via…

We study a certain type of action of categories on categories and on operads. Using the structure of the categories {\Delta} and {\Omega} governing category and operad structures, respectively, we define categories which instead encode the…

In this work, we address ergodicity of smooth actions of finitely generated semi-groups on an m-dimensional closed manifold M. We provide sufficient conditions for such an action to be ergodic with respect to the Lebesgue measure. Our…

First-order logic with dependent sorts, such as Makkai's first-order logic with dependent sorts (FOLDS), or Aczel's and Belo's dependently typed (intuitionistic) first-order logic (DFOL), may be regarded as logic enriched dependent type…

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 a previous paper [1] [MR4101040], we initiated a systematic study of semihypergroups and had a thorough discussion about some important analytic and algebraic objects associated to this class of objects. In this paper, we investigate…

This article studies a structural aspect of measure-preserving actions of products of countable discrete groups, involving a so-called 'synergodic decomposition' in terms of the ergodic components of the actions of the two factor groups. We…

The question whether there exists an integral solution to the system of linear equations with non-negative constraints, $A\x = \b, \, \x \ge 0$, where $A \in \Z^{m\times n}$ and ${\mathbf b} \in \Z^m$, finds its applications in many areas,…

We study quasiminimal classes, i.e. abstract elementary classes (AECs) that arise from a quasiminimal pregeometry structure. For these classes, we develop an independence notion, and in particular, a theory of independence in $\M^{eq}$. We…

Let G be a group and let P be a subsemigroup of G. In order to describe the crossed product of a C*-algebra A by an action of P by unital endomorphisms we find that we must extend the action to the whole group G. This extension fits into a…

In this article, we prove Neveu decomposition for the action of the locally compact amenable semigroup of positive contractions on semifinite von Neumann algebras and thus, it entirely resolves the problem for the actions of arbitrary…

Given a Frobenius category $\mathcal{F}$ satisfying certain finiteness conditions, we consider the localization of its Hall algebra $\mathcal{H(F)}$ at the classes of all projective-injective objects. We call it the {\it "semi-derived Hall…

We give a new categorical approach to the Halmos-von Neumann theorem for actions of general topological groups. As a first step, we establish that the categories of topological and measure-preserving irreducible systems with discrete…

In this note we present a complete computation of the topological K-theory of the reduced C*-algebra of a semidirect product of the form $\Gamma=\mathbb{Z}^n\rtimes_\rho\mathbb{Z}/2$ with no further assumptions about of the conjugacy action…