Palindromes and orderings in Artin groups

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dc.creatorDeloup, Florian
dc.date2004-10-11
dc.date2005-03-14
dc.date.accessioned2026-07-07T05:13:11Z
dc.date.available2026-07-07T05:13:11Z
dc.descriptionThe braid group $B_{n}$, endowed with Artin's presentation, admits two distinguished involutions. One is the anti-automorphism ${\rm{rev}}: B_{n} \to B_{n}$, $v \mapsto \bar{v}$, defined by reading braids in the reverse order (from right to left instead of left to right). Another one is the conjugation $τ:x \mapsto Δ^{-1}x Δ$ by the generalized half-twist (Garside element). More generally, the involution ${\rm{rev}}$ is defined for all Artin groups (equipped with Artin's presentation) and the involution $τ$ is defined for all Artin groups of finite type. A palindrome is an element invariant under rev. We classify palindromes and palindromes invariant under $τ$ in Artin groups of finite type. The tools are elementary rewriting and the construction of explicit left-orderings compatible with rev. Finally, we discuss generalizations to Artin groups of infinite type and Garside groups.
dc.description16 pages, 4 figures. Main result extended to Artin groups. simplification of classification of $τ$-invariant palindromes in finite Artin groups. Added references
dc.identifierhttps://arxiv.org/abs/math/0410275
dc.identifierhttp://arxiv.org/abs/math/0410275
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/72850
dc.subjectGeometric Topology
dc.subjectGroup Theory
dc.subject20F36
dc.titlePalindromes and orderings in Artin groups
dc.typetext

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