The cyclic sliding operation in Garside groups - Mathematics > Group TheoryReport as inadecuate




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Abstract: 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 cyclingand decycling operations. Cyclic sliding appears to be a more natural choice,simplifying the algorithms concerning conjugacy in Garside groups and havingnicer theoretical properties. We show, in particular, that if a super summitelement has conjugates which are -rigid- that is, which have a certainparticularly simple structure, then the optimal way of obtaining such a rigidconjugate through conjugation by positive elements is given by iterated cyclicsliding.



Author: Volker Gebhardt, Juan González-Meneses

Source: https://arxiv.org/







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