Related papers: Bruck decomposition for endomorphisms of quasigrou…
On subsets E of the Mandelbrot set M, homeomorphisms are constructed by quasi-conformal surgery. When the dynamics of quadratic polynomials is changed piecewise by a combinatorial construction, a general theorem yields the corresponding…
Let $f \colon X \to Y$ be a morphism of concentrated schemes. We characterize $f$-perfect complexes $\mathcal{E}$ as those such that the functor $\mathcal{E} \otimes^{\mathbf{L}}_X \mathbf{L} f^*-$ preserves bounded complexes. We prove, as…
Word-representable graphs, which are the same as semi-transitively orientable graphs, generalize several fundamental classes of graphs. In this paper we propose a novel approach to study word-representability of graphs using a technique of…
Rational semigroups were introduced by Hinkkanen and Martin as a generalization of the iteration of a single rational map. There has subsequently been much interest in the study of rational semigroups. Quasiregular semigroups were…
An m-endomorphism of a free semigroup is an endomorphism that sends every generator to a word of length at most m. Two m-endomorphisms are combinatorially equivalent if they are conjugate under an automorphism of the semigroup. In this…
A bounded automorphism of a field or a group with trivial approximate centre is definable. In an expansion of a field by a Pfaffian family F of additive endomorphisms such that algebraic closure in the expansion coincides with relative…
In this paper we study a certain class of polycyclic groups. We outline a method for constructing a poly-$\mathbb{Z}$ group $G_n$ by describing a process for selecting maps that are used to extend $G_i$ to $G_{i+1}$ for $1 \leq i \leq n-1$…
The monography examines the problem of constructing a group of automorphisms of a graph. A graph automorphism is a mapping of a set of vertices onto itself that preserves adjacency. The set of such automorphisms forms a vertex group of a…
In this paper, we define a new cohomology theory for multiplicative Hom-pre-Lie algebras which controls deformations of Hom-pre-Lie algebra structure. This new cohomology is a natural one by considering the structure map. We develop…
Quasi-logarithmic combinatorial structures are a class of decomposable combinatorial structures which extend the logarithmic class considered by Arratia, Barbour and Tavar\'{e} (2003). In order to obtain asymptotic approximations to their…
Given a quasi-reductive group $G$ over a local field $k$, using Berkovich geometry, we exhibit a family of $G(k)$-equivariant compactifications of the Bruhat-Tits building $\mathcal B(G, k)$, constructed and investigated by Solleveld and…
We introduce a quantum automorphism group for hypergraphs, which turns out to generalize the quantum automorphism group of Bichon for classical graphs. Further, we show that our quantum automorphism group acts on hypergraph C*-algebras as…
New expansionary and rotational quadratic forms are constructed for $E^n$-endomorphisms. Relations amongst the various eigenvalues, eigendirections and matrix invariants are established, including propositions on complexity and geometric…
Automorphisms of order $2$ are studied in order to understand generalized symmetric spaces. The groups of type $E_6$ we consider here can be realized as both the group of linear maps that leave a certain determinant invariant, and also as…
We describe general methods for enumerating subsemigroups of finite semigroups and techniques to improve the algorithmic efficiency of the calculations. As a particular application we use our algorithms to enumerate all transformation…
Let $G$ be a reductive algebraic group---possibly non-connected---over a field $k$ and let $H$ be a subgroup of $G$. If $G= GL_n$ then there is a degeneration process for obtaining from $H$ a completely reducible subgroup $H'$ of $G$; one…
Closed quantum surfaces of any genus are defined as subalgebras of the Toeplitz algebra by mimicking the classical construction of identifying arcs on the boundary of the (quantum) unit disk. Isomorphism classes obtained from different…
We study deformations of holomorphic maps of compact, complex, K\"ahler manifolds. In particular, we describe a generalization of Bloch's semiregularity map that annihilates obstructions to deform holomorphic maps with fixed codomain.
Let X be a closed surface of genus two embedded in the 3-sphere. Then X inherits a metric and an orientation, which give an almost complex structure, which automatically integrates to a genuine complex structure, making X a Riemann surface.…
This paper answers a question raised by Grothendieck in 1970 on the "Grothendieck closure" of an integral linear group and proves a conjecture of the first author made in 1980. This is done by a detailed study of the congruence topology of…