Related papers: Cluster braid groups of Coxeter-Dynkin diagrams

We extend our recent work on set-theoretic solutions of the Yang-Baxter or braid relations with new results about their automorphism groups, strong twisted unions of solutions and multipermutation solutions. We introduce and study graphs of…

Cluster algebras were introduced by Fomin-Zelevinsky in 2002 in order to give a combinatorial framework for phenomena occurring in the context of algebraic groups. Cluster algebras also have links to a wide range of other subjects,…

Recent work suggests that topological features of certain quantum gravity theories can be interpreted as particles, matching the known fermions and bosons of the first generation in the Standard Model. This is achieved by identifying…

We show that the change of basis matrices of a set of $m$ bases of a finite vector space is a connected groupoid of order $m^2$. We define a general method to express the elements of change of basis matrices as algebraic expressions using…

In this paper, we study the structure of braid graphs in simply-laced Coxeter systems. We prove that every reduced expression has a unique factorization as a product of so-called links, which in turn induces a decomposition of the braid…

We review the properties of the finite Coxeter groups which are most useful for applications to cohomological invariants, namely their classes of involutions and their "cubes" (abelian subgroups generated by reflections).

Points of an orbit of a finite Coxeter group G, generated by n reflections starting from a single seed point, are considered as vertices of a polytope (G-polytope) centered at the origin of a real n-dimensional Euclidean space. A general…

We introduce a switching operation, inspired by the Godsil-McKay switching, in order to obtain pairs of $G$-cospectral gain graphs, that are gain graphs cospectral with respect to every representation of the gain group $G$. For instance,…

For any finite Coxeter system $(W,S)$ we construct a certain noncommutative algebra, so-called {\it bracket algebra}, together with a familiy of commuting elements, so-called {\it Dunkl elements.} Dunkl elements conjecturally generate an…

We present a diagrammatic notation to derive the quantum-electrodynamic coupled cluster (QED-CC) equations needed for the description for polaritonic ground and excited states. Our presented notation is a generalization of the existing…

A new family of groups, called trickle groups, is presented. These groups generalize right-angled Artin and Coxeter groups, as well as cactus groups. A trickle group is defined by a presentation with relations of the form $xy = zx$ and…

In order to construct solutions of the braid equation we consider bijective left non-degenerate set-theoretic type solutions, which correspond to regular q-cycle coalgebras. We obtain a partial classification of the different q-cycle…

We give criteria for deciding whether or not a triangle-free simple graph is the presentation graph of a right-angled Coxeter group that is quasiisometric to some right-angled Artin group, and, if so, producing a presentation graph for such…

There is a procedure, due to Dani and Levcovitz, for taking a finite simplicial graph (\Gamma) and a subgraph (\Lambda) of its complement, checking some conditions, and, if satisfied, producing a graph (\Delta) such that the right-angled…

We construct finite volume hyperbolic manifolds with large symmetry groups. The construction makes use of the presentations of finite Coxeter groups provided by Barot and Marsh and involves mutations of quivers and diagrams defined in the…

We study a quotient of the group algebra of the braid group in which the Artin generators satisfy a cubic relation. This quotient is maximal among the ones satisfying such a cubic relation. It is finite-dimensional for at least n at most 5…

We suggest a cohomological framework to describe groups of $I$-type and involutive Yang-Baxter groups. These groups are key in the study of involutive non-degenerate set-theoretic solutions of the quantum Yang-Baxter equation. Our main tool…

We consider the homology theory of \'etale groupoids introduced by Crainic and Moerdijk, with particular interest to groupoids arising from topological dynamical systems. We prove a K\"unneth formula for products of groupoids and a…

This paper is a following to math.RT/0410454. For a finite group of Lie type we study the endomorphisms, commuting with the group action, of a Deligne-Lusztig variety associated to a regular element of the Weyl group. We state some general…

In 2011 Eriko Hironaka introduced an interesting generalization of Coxeter groups, motivated by studying certain mapping classes. The generalization is by labeling the vertices of a Coxeter graph either by +1 or by -1, and then generalizing…