منابع مشابه
Garside monoids vs divisibility monoids
Divisibility monoids (resp. Garside monoids) are a natural algebraic generalization of Mazurkiewicz trace monoids (resp. spherical Artin monoids), namely monoids in which the distributivity of the underlying lattices (resp. the existence of common multiples) is kept as an hypothesis, but the relations between the generators are not supposed to necessarily be commutations (resp. be of Coxeter ty...
متن کاملGarside Structure on Monoids with Quadratic Square-free Relations
We show the intimate connection between various mathematical notions that are currently under active investigation: a class of Garside monoids, with a “nice” Garside element, certain monoids S with quadratic relations, whose monoidal algebra A = kS has a Frobenius Koszul dual A with regular socle, the monoids of skew-polynomial type (or equivalently, binomial skew-polynomial rings) which were i...
متن کاملAlternating Normal Forms for Braids and Locally Garside Monoids
We describe new types of normal forms for braid monoids, Artin– Tits monoids, and, more generally, all monoids in which divisibility has some convenient lattice properties (“locally Garside monoids”). We show that, in the case of braids, one of these normal forms turns out to coincide with the normal form introduced by Burckel and deduce that the latter can be computed easily. This approach lea...
متن کاملDual Garside Structure of Braids and Free Cumulants of Products
We count the n-strand braids whose normal decomposition has length at most 2 in the dual braid monoid B n by reducing the question to a computation of free cumulants for a product of independent variables, for which we establish a general formula.
متن کاملOn graph products of automatic monoids
The graph product is an operator mixing direct and free products. It is already known that free products and direct products of automatic monoids are automatic. The main aim of this paper is to prove that graph products of automatic monoids of finite geometric type are still automatic. A similar result for prefix-automatic monoids
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ژورنال
عنوان ژورنال: Mathematische Zeitschrift
سال: 2015
ISSN: 0025-5874,1432-1823
DOI: 10.1007/s00209-015-1542-4