The cyclic sliding operation in Garside groups

We present a new operation to be performed on elements in a Garside group, called cyclic sliding, which is introduced to replace the well known cycling and decycling operations. Cyclic sliding appears to be a more natural choice, simplifying the algorithms concerning conjugacy in Garside groups and...

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Detalhes bibliográficos
Autores: Gebhardt, Volker, González-Meneses López, Juan
Tipo de documento: artigo
Estado:Versão publicada
Data de publicação:2010
País:España
Recursos:Universidad de Sevilla (US)
Repositório:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/42284
Acesso em linha:http://hdl.handle.net/11441/42284
https://doi.org/10.1007/s00209-009-0502-2
Access Level:Acceso aberto
Palavra-chave:Garside groups
conjugacy
cyclic
sliding
sliding circuits
ultra summit set
Descrição
Resumo:We present a new operation to be performed on elements in a Garside group, called cyclic sliding, which is introduced to replace the well known cycling and decycling operations. Cyclic sliding appears to be a more natural choice, simplifying the algorithms concerning conjugacy in Garside groups and having nicer theoretical properties. We show, in particular, that if a super summit element has conjugates which are rigid (that is, which have a certain particularly simple structure), then the optimal way of obtaining such a rigid conjugate through conjugation by positive elements is given by iterated cyclic sliding.