The language of geodesics for Garside groups
R Charney, J Meier - Mathematische Zeitschrift, 2004 - Springer
R Charney, J Meier
Mathematische Zeitschrift, 2004•Springer… 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. …
Garside monoids satisfy Ore’s criterion, hence they embed in their group of fractions, and thus
we may define a Garside group to be the group of fractions of a Garside monoid. We denote a …
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. …
Garside monoids satisfy Ore’s criterion, hence they embed in their group of fractions, and thus
we may define a Garside group to be the group of fractions of a Garside monoid. We denote a …
Abstract
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.
Springer
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