Quasi-reflection algebras and cyclotomic associators
| dc.creator | Enriquez, B. | |
| dc.date | 2004-08-03 | |
| dc.date | 2007-10-17 | |
| dc.date.accessioned | 2026-07-07T08:36:42Z | |
| dc.date.available | 2026-07-07T08:36:42Z | |
| dc.description | We 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.description | 52 pages | |
| dc.identifier | https://arxiv.org/abs/math/0408035 | |
| dc.identifier | http://arxiv.org/abs/math/0408035 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/140156 | |
| dc.subject | Quantum Algebra | |
| dc.subject | Number Theory | |
| dc.title | Quasi-reflection algebras and cyclotomic associators | |
| dc.type | text |