Related papers: An elegant 3-basis for inverse semigroups
Algorithmic methods for the explicit inversion of the indefinite double covering maps are proposed. These are based on either the Givens decomposition or the polar decomposition of the given matrix in the proper, indefinite orthogonal group…
Recently we have shown that the equivalence classes of metrics on the double of a metric space $X$ form an inverse semigroup. Here we define an inverse subsemigroup related to a family of isometric subspaces of $X$, which is more…
We argue that weak containment is an appropriate notion of amenability for inverse semigroups. Given an inverse semigroup $S$ and a homomorphism $\phi$ of $S$ onto a group $G$, we show, under an assumption on $\ker(\phi)$, that $S$ has weak…
Consider the Jacobi operators $\cJ$ given by $(\cJ y)_n=a_ny_{n+1}+b_ny_n+a_{n-1}^*y_{n-1}$, $y_n\in \C^m$ (here $y_0=y_{p+1}=0$), where $b_n=b_n^*$ and $a_n:\det a_n\ne 0$ are the sequences of $m\ts m$ matrices, $n=1,..,p$. We study two…
We give an algebraic characterisation of ordered groupoids, namely, we show that there is a categorical isomophism between the category of ordered groupoids and the category of $D$-inverse constellations. Here constellations are partial…
For semigroup $S$, a commutative congruence $\sigma_{orient}$ on $S$ and a subsemigroup Orientable($S$) of $S$ were introduced in "Two cancellative commutative congruences and group diagrams", Semigroup Forum (2011) 82: 338-353. Here we…
The invariance identity involving three operations $D_{f,g}:X\times X\rightarrow X$ of the form \begin{equation*} D_{f,g}\left( x,y\right) =\left( f\circ g\right) ^{-1}\left( f\left( x\right) \oplus g\left( y\right) \right) \text{,}…
We study the relationship between Bell states, finite groups and complete sets of bases. We show how to obtain a set of N+1 bases in which Bell states are invariant. They generalize the X, Y and Z qubit bases and are associated to groups of…
We prove an inverse theorem for the Gowers $U^2$-norm for maps $G\to\mathcal M$ from an countable, discrete, amenable group $G$ into a von Neumann algebra $\mathcal M$ equipped with an ultraweakly lower semi-continuous, unitarily invariant…
We define the notion of a partial action on a generalized Boolean algebra and associate to every such system and commutative unital ring $R$ an $R$-algebra. We prove that every strongly $E^{\ast}$-unitary inverse semigroup has an associated…
This is the second paper devoted to the numerical version of Signature-inverse Theorem in terms of the underlying joint invariants. Signature Theorem and its Inverse guarantee any application of differential invariant signature curves to…
A twist property is developed which imparts certain properties on the twisted group algebra. These include an involution * satisfying (xy)*=y*x* and an inner product satisfying <xy,z> = <x,zy*> and <xy,z>=<y,x*z>. Examples of twisted group…
Motivated by recent appearance of multivalued structures in categorification, tropical geometry and other areas, we study basic properties of abstract multisemigroups. We give many new and old examples and general constructions for…
It is known to experts that certain regular inclusions of von Neumann algebras arise as crossed products with cocycle actions of the canonical quotient groupoids associated with the inclusions. Similarly, `strongly normal' inclusions of…
We construct a completely normal bounded distributive lattice D in which for every pair (a, b) of elements, the set {x $\in$ D | a $\le$ b $\lor$ x} has a countable coinitial subset, such that D does not carry any binary operation -…
We introduce a concept of approximately invertible elements in non-unital normed algebras which is, on one side, a natural generalization of invertibility when having approximate identities at hand, and, on the other side, it is a direct…
We present the weighted weak group inverse, which is a new generalized inverse of operators between two Hilbert spaces, introduced to extend weak group inverse for square matrices. Some characterizations and representations of the weighted…
The main result of this paper is to show that all binomial identities are orderable. This is a natural statement in the combinatorial theory of finite sets, which can also be applied in distributed computing to derive new strong bounds on…
Let $\mathbb{H}$ be the general, reduced Heisenberg group. Our main result establishes the inverse-closedness of a class of integral operators acting on $L^{p}(\mathbb{H})$, given by the off-diagonal decay of the kernel. As a consequence of…
The semigroup $B_0$ is the only, up to isomorphism, 4-element subsemigroup of the 5-element Brandt semigroup $B_2$. Being an inverse semigroup, the semigroup $B_2$ can naturally be considered an additively idempotent semiring and $B_0$ is…