Garside structures for ( some more ) Artin groups
نویسندگان
چکیده
منابع مشابه
Dual Euclidean Artin Groups and the Failure of the Lattice Property
The irreducible euclidean Coxeter groups that naturally act geometrically on euclidean space are classified by the well-known extended Dynkin diagrams and these diagrams also encode the modified presentations that define the irreducible euclidean Artin groups. These Artin groups have remained mysterious with some exceptions until very recently. Craig Squier clarified the structure of the three ...
متن کاملParabolic subgroups of Garside groups
A Garside monoid is a cancellative monoid with a finite lattice generating set; a Garside group is the group of fractions of a Garside monoid. The family of Garside groups contains the Artin-Tits groups of spherical type. We generalise the well-known notion of a parabolic subgroup of an Artin-Tits group into that of a parabolic subgroup of a Garside group. We also define the more general notion...
متن کاملAn Introduction to Combinatorial Garside Structures
The notion of a Garside group was first introduced in a paper of Dehornoy and Paris [14]. Over the past decade they have been used as a tool to better understand the structure of Artin’s braid groups [2] and their generalizations. In general, one can use the Garside structure associated with a Garside group to solve the word and conjugacy problems, as well as create a finite dimensional Eilenbe...
متن کاملGaussian groups and Garside groups, two generalisations of Artin groups
It is known that a number of algebraic properties of the braid groups extend to arbitrary finite Coxeter type Artin groups. Here we show how to extend the results to more general groups that we call Garside groups. Define a Gaussian monoid to be a finitely generated cancellative monoid where the expressions of a given element have bounded lengths, and where left and right lower common multiples...
متن کاملPalindromes and Orderings in Artin Groups
The braid group Bn, endowed with Artin’s presentation, admits two distinguished involutions. One is the anti-automorphism rev : Bn → Bn, v 7→ v̄, defined by reading braids in the reverse order (from right to left instead of left to right). Another one is the conjugation τ : x 7→ ∆x∆ by the generalized half-twist (Garside element). More generally, the involution rev is defined for all Artin group...
متن کامل