Related papers: A note on Boolean inverse monoids and ample groupo…
We prove a nearly polynomial inverse theorem for the Gowers $U^d$ norm, over finite fields of non-small characteristic, for polynomials of degree $d+1$. The case of degree $d$ was very recently settled by Mili\'{c}evi\'{c} and…
This note records the order of a higher dimensional Dehn twist in a range of topologically significant groups.
In this paper, we introduce a new concept called left (right) g-MP inverse in a $*$-monoid. The relations of this type of generalized inverse with left inverse along an element are investigated. Also, the reverse order law for the inverse…
In this short note we show the existence of an epimorphism between groups of $2$-bridge knots by means of an elementary argument using the Riley polynomial. As a corollary, we give a classification of $2$-bridge knots by Riley polynomials.
New cases of the multiplicity conjecture are considered.
A problem involving a square in the curvilinear triangle made by two touching congruent circles and their common tangent is generalized.
A review of the inverse scattering transform is given, and an introduction to solitons is provided.
We investigate the groups of units of one-relator and special inverse monoids. These are inverse monoids which are defined by presentations where all the defining relations are of the form $r=1$. We develop new approaches for finding…
The main goal of this note is to provide a new proof of a classical result about projectivities between finite abelian groups. It is based on the concept of fundamental group lattice, studied in our previous papers \cite{8} and \cite{9}. A…
There are well known relations between braid groups and symmetric groups, between Artin-Briskorn braid groups and Coxeter groups. Inverse braid monoid the same way is related to the inverse symmetric monoid. In the paper we show that…
Boole polynomials play an important role in the area of number theory, algebra and umbral calculus. In this paper, we investigate some properties of Boole polynomials and consider Witt-type formulas for the Boole numbers and polynomials.…
These notes deal with a few aspects of Lie algebras and Lie groups, including some matters related to exponentiation.
We revisit our construction of the Thompson groups from the polycyclic inverse monoids in the light of new research. Specifically, we prove that the Thompson group $G_{n,1}$ is the group of units of a Boolean inverse monoid $C_{n}$ called…
The paper presents a counterexample to the Hodge conjecture.
We provide an explicit construction of quasi-invariant measures on polarized coadjoint orbits of a Lie group G. The use of specific (trivial) central extensions of G by the multiplicative group ${R}^+$ allows us to restore the strict…
We provide a unified treatment of several results concerning full groups of ample groupoids and paradoxical decompositions attached to them. This includes a criterion for the full group of an ample groupoid being amenable as well as…
We show that each connected group scheme of finite type over an arbitrary ground field is isomorphic to the component of the identity inside the automorphism group scheme of some projective, geometrically integral scheme. The main…
An infinite family of Boolean polynomials which correspond to the discrete average maps, defined in [2], is constructed and their algebraic and combinatorial properties are investigated. They turn out to be balanced, and some recurrence…
We study a non-commutative generalization of Stone duality that connects a class of inverse semigroups, called Boolean inverse $\wedge$-semigroups, with a class of topological groupoids, called Hausdorff Boolean groupoids. Much of the paper…
This paper is the second in a series investigating cartesian closed varieties. In first of these, we showed that every non-degenerate finitary cartesian variety is a variety of sets equipped with an action by a Boolean algebra B and a…