Related papers: E-semigroups over closed convex cones
Interest in Riemannian manifolds with holonomy equal to the exceptional Lie group $\mathrm{G}_2$ have spurred extensive research in geometric flows of $\mathrm{G}_2$-structures defined on seven-dimensional manifolds in recent years. Among…
Model sets play a fundamental role in structure analysis of quasicrystals. The diffraction diagram of a quasicrystal admits as symmetry group a finite group G, and there is a G-cluster C (union of orbits of G) such that the quasicrystal can…
In a recent work of Matteo Mio on compact quantitative equational theories (here compact means that all its consequences are derivable by means of finite proofs) convex algebras on the carrier set [0,1] whose operations are monotone and…
A scale-multiplicative semigroup in a totally disconnected, locally compact group $G$ is one for which the restriction of the scale function on $G$ is multiplicative. The maximal scale-multiplicative semigroups in groups acting…
We investigate the structure of isometric subgraphs of hypercubes (i.e., partial cubes) which do not contain finite convex subgraphs contractible to the 3-cube minus one vertex $Q^-_3$ (here contraction means contracting the edges…
The isomorphism of 0-homology groups of a categorical at zero semigroup and homology groups of its 0-reflector is proved. Some applications of 0-homology to Eilenberg-MacLane homology of semigroups are given.
Many questions at the core of graph theory can be formulated as questions about certain group-valued flows: examples are the cycle double cover conjecture, Berge-Fulkerson conjecture, and Tutte's 3-flow, 4-flow, and 5-flow conjectures. As…
Given a group G, we construct, in a canonical way, an inverse semigroup S(G) associated to G. The actions of S(G) are shown to be in one-to-one correspondence with the partial actions of G, both in the case of actions on a set, and that of…
In this note, an intrinsic description of some families of linear codes with symmetries is given, showing that they can be described more generally as quasi group codes, that is, as linear codes allowing a group of permutation automorphisms…
In this paper, we study the geometry of cone-offs of CAT(0) cube complexes over a family of combinatorially convex subcomplexes, with an emphasis on their Gromov-hyperbolicity. A first application gives a direct cubical proof of the…
In the paper we describe the group $\mathbf{Aut}\left(\mathscr{C}_{\mathbb{Z}}\right)$ of automorphisms of the extended bicyclic semigroup $\mathscr{C}_{\mathbb{Z}}$ and study the variants $\mathscr{C}_{\mathbb{Z}}^{m,n}$ of the extended…
The coadjoint representation of a connected algebraic group $Q$ with Lie algebra $\mathfrak q$ is a thrilling and fascinating object. Symmetric invariants of $\mathfrak q$ (= $\mathfrak q$-invariants in the symmetric algebra $S(\mathfrak…
We define a class of not necessarily linear $C_0$-semigroups $(P_t)_{t\geq0}$ on $C_b(E)$ (more generally, on $C_\kappa(E):=\frac1\kappa C_b(E)$, for some bounded function $\kappa$, which is the pointwise limit of a decreasing sequence of…
This paper enriches the list of known properties of congruence sequences starting from the universal relation and successively performing the operators lower $k$ and lower $t$. Two series of inverse semigroups, namely…
Since its introduction by Symons, the semigroup of maps with restricted range has been studied in the context of transformations on a set, or of linear maps on a vector space. Sets and vector spaces being particular examples of independence…
In this paper we show some results on homogeneous CR manifolds, proved by introducing their associated CR algebras. In particular, we give different notions of nondegeneracy (generalizing the usual notion for the Levi form) which correspond…
From any directed graph $E$ one can construct the graph inverse semigroup $G(E)$, whose elements, roughly speaking, correspond to paths in $E$. Wang and Luo showed that the congruence lattice $L(G(E))$ of $G(E)$ is upper-semimodular for…
We associate cube complexes called completions to each subgroup of a right-angled Coxeter group (RACG). A completion characterizes many properties of the subgroup such as whether it is quasiconvex, normal, finite-index or torsion-free. We…
We prove well-posedness for very general linear wave- and diffusion equations on compact or non-compact metric graphs allowing various different conditions in the vertices. More precisely, using the theory of strongly continuous operator…
A C*-algebra containing the CCR and CAR algebras as its subalgebras and naturally described as the semidirect product of these algebras is discussed. A particular example of this structure is considered as a model for the algebra of…