The language of geodesics for Garside groups
نویسندگان
چکیده
منابع مشابه
The Language of Geodesics for Garside Groups
We prove that the language of all geodesics of any Garside group, with respect to the generating set of divisors of the Garside element, forms a regular language. In particular, the braid groups admit generating sets where the associated language of geodesics is regular.
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We solve the subgroup conjugacy problem for parabolic subgroups and Garside subgroups of a Garside group, and we present deterministic algorithms. This solution may be improved by using minimal simple elements. For standard parabolic subgroups of Garside groups we provide e ective algorithms for computing minimal simple elements.
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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...
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We present a new algorithm to solve the conjugacy problem in Artin braid groups, which is faster than the one presented by Birman, Ko and Lee [3]. This algorithm can be applied not only to braid groups, but to all Garside groups (which include finite type Artin groups and torus knot groups among others).
متن کاملA New Garside Structure for Braid Groups
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 structure. A detailed study of the combinatorics of this structure leads us to describe it as post-classical.
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ژورنال
عنوان ژورنال: Mathematische Zeitschrift
سال: 2004
ISSN: 0025-5874,1432-1823
DOI: 10.1007/s00209-004-0666-8