Garside families and Garside germs
نویسندگان
چکیده
منابع مشابه
Garside 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...
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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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Garside calculus is the common mechanism that underlies a certain type of normal form for the elements of a monoid, a group, or a category. Originating from Garside’s approach to Artin’s braid groups, it has been extended to more and more general contexts, the latest one being that of categories and what are called Garside families. One of the benefits of this theory is to lead to algorithms so...
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We describe how an Ore category with a Garside family can be used to construct a classifying space for its fundamental group(s). The construction simultaneously generalizes Brady’s classifying space for braid groups and the Stein–Farley complexes used for various relatives of Thompson’s groups. It recovers the fact that Garside groups have finite classifying spaces. We describe the categories a...
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Building on a result by W.Rump, we show how to exploit the right-cyclic law (xy)(xz) = (yx)(yz) in order to investigate the structure groups and monoids attached with (involutive nondegenerate) set-theoretic solutions of the Yang–Baxter equation. We develop a sort of right-cyclic calculus, and use it to obtain short proofs for the existence both of the Garside structure and of the I-structure o...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 2013
ISSN: 0021-8693
DOI: 10.1016/j.jalgebra.2013.01.026