相关论文: Interval exchanges that do not embed in free group…
We construct ensembles of random integrable matrices with any prescribed number of nontrivial integrals and formulate integrable matrix theory (IMT) -- a counterpart of random matrix theory (RMT) for quantum integrable models. A type-M…
Rauzy-type dynamics are group actions on a collection of combinatorial objects. The first and best known example concerns an action on permutations, associated to interval exchange transformations (IET) for the Poincar\'e map on compact…
We examine maps between noncommutative projective spaces. A surjection of graded rings A-->A/J induces a closed immersion Proj(A/J)-->Proj(A). A homomorphism f:A-->B between graded rings induces an affine map U --> Proj(A) from a non-empty…
We consider compact matrix quantum groups whose $N$-dimensional fundamental representation decomposes into an $(N-1)$-dimensional and a one-dimensional subrepresentation. Even if we know that the compact matrix quantum group associated to…
We study internal Lie algebras in the category of subshifts on a fixed group -- or Lie algebraic subshifts for short. We show that if the acting group is virtually polycyclic and the underlying vector space has dense homoclinic points, such…
In an alternative interpretation, the Seiberg-Witten map is shown to be induced by a field dependent co-ordinate transformation connecting noncommutative and ordinary space-times. Furthermore, following our previous ideas, it has been…
A non-Abelian analogue of the Abelian T-duality momentum-winding exchange is described. The non-Abelian T-duality relates $\sigma$-models living on the cosets of a Drinfeld double with respect to its isotropic subgroups. The role of the…
A domain exchange map (DEM) is a dynamical system defined on a smooth Jordan domain which is a piecewise translation. We explain how to use cut-and-project sets to construct minimal DEMs. Specializing to the case in which the domain is a…
Various authors have been generalizing some unital ring properties to nonunital rings. We consider properties related to cancellation of modules (being unit-regular, having stable range one, being directly finite, exchange, or clean) and…
We say that the sequence $g_n$, $n\ge 3$, $n \rightarrow \infty$ of polynomial transformation bijective maps of free module $K^n$ over commutative ring $K$ is a sequence of stable degree if the order of $g_n$ is growing with $n$ and the…
We consider tilings of Euclidean spaces by polygons or polyhedra, in particular, tilings made by a substitution process, such as the Penrose tilings of the plane. We define an isomorphism invariant related to a subgroup of rotations and…
In this paper, we consider the problem of formal iteration. We construct an area preserving mapping which does not have any square root. This leads to a counterexample to Moser's existence theorem for an interpolation problem. We give…
In this paper, we extend the iterated integrals from smooth manifolds to digraphs and develop the associated algebraic and geometric structures. Iterated integrals on a digraph naturally give rise to the iterated path algebra and the…
For any right-angled Artin group, we show that its outer automorphism group contains either a finite-index nilpotent subgroup or a nonabelian free subgroup. This is a weak Tits alternative theorem. We find a criterion on the defining graph…
This paper presents a general and systematic discussion of various symbolic representations of iterated maps through subshifts. We give a unified model for all continuous maps on a metric space, by representing a map through a general…
The power graph of a group $G$ is a graph with vertex set $G$, in which two vertices are adjacent if one is some power of the other. In the commuting graph, with $G$ as the vertex set, two vertices are joined by an edge if they commute in…
The competition graph of a doubly partial order is known to be an interval graph. The competition-common enemy graph of a doubly partial order is also known to be an interval graph unless it contains a cycle of length 4 as an induced…
A relationally exchangeable structure is a random combinatorial structure whose law is invariant with respect to relabeling its relations, as opposed to its elements. Aside from exchangeable random partitions, examples include edge…
We relate the Mather invariant of diffeomorphisms of the (closed) interval to their asymptotic distortion. For maps with only parabolic fixed points, we show that the former is trivial if and only if the latter vanishes. As a consequence,…
We describe all possible bimodal over-twist patterns. In particular, we give an algorithm allowing one to determine what the left endpoint of the over-rotation interval of a given bimodal map is. We then define a new class of polymodal…