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Garside families and Garside germs. (English) Zbl 1294.18003
Summary: 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.

MSC:
18B40 Groupoids, semigroupoids, semigroups, groups (viewed as categories)
20F10 Word problems, other decision problems, connections with logic and automata (group-theoretic aspects)
20F36 Braid groups; Artin groups
20M05 Free semigroups, generators and relations, word problems
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