Related papers: Garside and quadratic normalisation: a survey
We describe a new presentation for the complex reflection groups of type $(e,e,r)$ and their braid groups. A diagram for this presentation is proposed. The presentation is a monoid presentation which is shown to give rise to a Garside…
A recently introduced real space renormalization group technique, developed for the analysis of processes in the Kardar-Parisi-Zhang universality class, is generalized and tested by applying it to a different family of surface growth…
We analyse the normal quotient structure of several infinite families of finite connected edge-transitive, four-valent oriented graphs. These families were singled out by Marusic and others to illustrate various different internal…
Extending the methods from our previous work on quantum knots and quantum graphs, we describe a general procedure for quantizing a large class of mathematical structures which includes, for example, knots, graphs, groups, algebraic…
Determining whether an arbitrary subring $R$ of $k[x_1^{\pm 1},\dots, x_n^{\pm 1}]$ is a normal domain is, in general, a nontrivial problem, even in the special case of a monomial generated domain. In this paper, we provide a complete…
M. Picantin introduced the notion of Garside groups of spindle type, generalizing the 3-strand braid group. We show that, for linear Garside groups of spindle type, a normal form and a solution to the conjugacy problem are logspace…
An element in Artin's braid group B_n is said to be periodic if some power of it lies in the center of B_n. In this paper we prove that all previously known algorithms for solving the conjugacy search problem in B_n are exponential in the…
We give an introduction to renormalisation, focusing first on a pedagogical description of fundamental concepts of the procedure and its features, then we introduce the renormalisation group and its equations. We discuss then the case of…
We give some results on quadratic normality of reducible curves canonically embedded and partially extend this study to their projective normality.
We construct a new monoid structure for Artin groups associated with finite Coxeter systems. This monoid shares with the classical positive braid monoid a crucial algebraic property: it is a Garside monoid. The analogy with the classical…
We define and study the Picard group of a monoid scheme and the class group of a normal monoid scheme. To do so, we develop some ideal theory for (pointed abelian) noetherian monoids, including primary decomposition and discrete valuations.…
Renormalizability of the (minimal) single-fermion QED extension is investigated at all orders of perturbation theory in the framework of algebraic renormalization, a regularization-independent method. Relative to the standard QED, new…
In this paper, we give a Groebner-Shirshov basis of the braid group $B_{n+1}$ in the Artin--Garside generators. As results, we obtain a new algorithm for getting the Garside normal form, and a new proof that the braid semigroup $B^+{n+1}$…
We describe presentations of braid groups of type $A$ arising from coloured quivers of mutation type $A$. We show that these can be interpreted geometrically as generalised triangulations of regular polygons.
We present various new results on greedoids. We prove a theorem that generalizes an equivalent formulation of Edmonds' classic matroid polytope theorem to local forest greedoids -- a class of greedoids that contains matroids as well as…
We determine the quantized function algebras associated with various examples of generalized sine-Gordon models. These are quadratic algebras of the general Freidel-Maillet type, the classical limits of which reproduce the lattice Poisson…
Braids can be represented geometrically as laminations of punctured disks. The geometric complexity of a braid is the minimal complexity of a lamination that represents it, and tight laminations are representatives of minimal complexity.…
I am showing how the ideas behind the renormalisation group can be generalised in order to produce the desired reduction in the degrees of freedom other that the ones considered up to now. Instead of looking only at the renormalisation…
We construct a quasi-Garside monoid structure for the free group. This monoid should be thought of as a dual braid monoid for the free group, generalising the constructions by Birman-Ko-Lee and by the author of new Garside monoids for Artin…
We show that any normal algebraic monoid is an extension of an abelian variety by a normal affine algebraic monoid. This extends (and builds on) Chevalley's structure theorem for algebraic groups.