Tame Garside monoids
نویسندگان
چکیده
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 کاملGarside families and Garside germs
Garside families have recently emerged as a relevant context for extending results involving Garside monoids and groups, which themselves extend the classical theory of (generalized) braid groups. Here we establish various characterizations of Garside families, that is, equivalently, various criteria for establishing the existence of normal decompositions of a certain type. In 1969, F.A.Garside...
متن کاملGarside Families in Artin–tits Monoids and Low Elements in Coxeter Groups
where both terms consist of two alternating letters and have the same length. First investigated by J.Tits in the late 1960s [2], and then in [3] and [11], these groups remain incompletely understood, with many open questions, including the decidability of the Word Problem in the general case [6]. The only well understood case is the one of spherical type, which is the case when the associated ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Algebra
سال: 2004
ISSN: 0021-8693
DOI: 10.1016/j.jalgebra.2004.07.014