Quasi-reflection algebras and cyclotomic associators

dc.creatorEnriquez, B.
dc.date2004-08-03
dc.date2007-10-17
dc.date.accessioned2026-07-07T08:36:42Z
dc.date.available2026-07-07T08:36:42Z
dc.descriptionWe develop a cyclotomic analogue of the theory of associators. Using a trigonometric version of the universal KZ equations, we prove the formality of a morphism B_n^1 -> (ZZ/N ZZ)^n rtimes S_n, where B_n^1 is a braid group of type B. The formality isomorphism depends algebraically on a series Psi_KZ, the ``KZ pseudotwist''. We study the scheme of pseudotwists and show that it is a torsor under a group GTM(N,k), mapping to Drinfeld's group GT(k), and whose Lie algebra is isomorphic to its associated graded grtm(N,k). We prove that Ihara's subgroup GTK of the Grothendieck-Teichmüller group, defined using distribution relations, in fact coincides with it. We show that the subscheme of pseudotwists satisfying distribution relations is a subtorsor. We study the corresponding analogue grtmd(N,k) of grtm(N,k); it is a graded Lie algebra with an action of (ZZ/N ZZ)^*, and we give a lower bound for the character of its space of generators.
dc.description52 pages
dc.identifierhttps://arxiv.org/abs/math/0408035
dc.identifierhttp://arxiv.org/abs/math/0408035
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/140156
dc.subjectQuantum Algebra
dc.subjectNumber Theory
dc.titleQuasi-reflection algebras and cyclotomic associators
dc.typetext

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