Related papers: Comment "On dual ordered semigroups"
Observations on rational Chow groups and cycle class maps in equivariant contexts.
A subsemigroup $S$ of an inverse semigroup $Q$ is a left I-order in $Q$ if every element in $Q$ can be written as $a^{-1}b$ where $a,b \in S$ and $a^{-1}$ is the inverse of $a$ in the sense of inverse semigroup theory. If we insist on $a$…
Quasitoric spaces were introduced by Davis and Januskiewicz in their 1991 Duke paper. There they extensively studied topological invariants of quasitoric manifolds. These manifolds are generalizations or topological counterparts of…
We consider exponential ultradistribution semigroups with non--densely defined generators and give structural theorems for ultradistribution semigroups. Also structural theorems for exponential ultradistribution semigroups are given.
Distributivity in algebraic structures appeared in many contexts such as in quasigroup theory, semigroup theory and algebraic knot theory. In this paper we give a survey of distributivity in quasigroup theory and in quandle theory.
This paper serves as an extended road map for our long-term project "Mixed Random-quasiperiodic Cocycles" [arXiv:2201.04745, arXiv:2109.09544, arXiv:2210.16908, 6, 7] with Pedro Duarte and Silvius Klein. Despite exhibiting totally different…
This thesis is dedicated to developing a dilation theory for semigroups of completely positive maps. The first part treats two-parameter semigroups, and contains also contributions to dilation theory of product system representations. The…
This paper proposes a novel deep learning approach for learning operators in semigroup, with applications to modeling unknown autonomous dynamical systems using time series data collected at varied time lags. It is a sequel to the previous…
This is a survey article on the recent developments of semipositivity, injectivity, and vanishing theorems for higher-dimensional complex projective varieties.
This paper studies Young diagrams of symmetric and pseudo-symmetric numerical semigroups and describes new operations on Young diagrams as well as numerical semigroups. These provide new decompositions of symmetric and pseudo-symmetric…
We generalise the work of Segre (1965), Cameron - Goethals - Seidel (1978), and Vanhove (2011) by showing that nontrivial $m$-ovoids of the dual polar spaces $DQ(2d, q)$, $DW(2d-1,q)$ and $DH(2d-1,q^2)$ ($d\ge 3$) are hemisystems. We also…
There is a mathematical error in the first version of this paper. A new corrected version will be posted when the error is fixed, possibly with a modified title.
This article introduces patterns of ideals of numerical semigroups, thereby unifying previous definitions of patterns of numerical semigroups. Several results of general interest are proved. More precisely, this article presents results on…
We develop a quantum duality principle for coisotropic subgroups of a (formal) Poisson group and its dual: namely, starting from a quantum coisotropic subgroup (for a quantization of a given Poisson group) we provide functorial recipes to…
We give an overview of various prolongations of quasigroups. Two step prolongation procedure is proposed.
We define the concentration of a numerical semigroup $S$ as $\mathsf{C}(S)=\max \left\{\text{next}_S(s)-s ~|~ s\in S \backslash \{0\}\right\}$ wherein $\text{next}_S(s)=\min\left\{x \in S ~|~ s<x\right\}$. In this paper, we study the class…
In this paper, we describe a complete computer classification of the hemisystems in the two known flock generalized quadrangles of order $(5^2,5)$ and give numerous further examples of hemisystems in all the known flock generalized…
By reformulating a learning process of a set system L as a game between Teacher (presenter of data) and Learner (updater of the abstract independent set), we define the order type dim L of L to be the order type of the game tree. The theory…
A recent paper of Trandafir and Cabello [Phys. Rev. A, 111, 022408 (2025)] contains a number of errors, inconsistencies, and inefficiencies. They are too numerous to be listed here, so we identify and discuss them in the main body of the…
We examine, in a general setting, a notion of inverse semigroup of left quotients, which we call left I-quotients. This concept has appeared, and has been used, as far back as Clifford's seminal work describing bisimple inverse monoids in…