We give a general definition of branched, self-similar Lie algebras, and show that important examples of Lie algebras fall into that class. We give sufficient conditions for a self-similar Lie algebra to be nil, and prove in this manner that the self-similar algebras associated with Grigorchuk’s and Gupta–Sidki’s torsion groups are nil as well as self-similar.We derive the same results for a class of examples constructed by Petrogradsky, Shestakov and Zelmanov.
Étant donnés un système de racines d’une des familles A, B, C, D, F, G et le groupe abélien libre qu’il engendre, on calcule explicitement la série de croissance de ce groupe relativement à Les résultats s’interprètent en termes du polynôme d’Ehrhart de l’enveloppe convexe de .
In questo lavoro studiamo i non CC-gruppi monolitici con tutti i quozienti propri CC-gruppi, che hanno sottogruppi abeliani normali non banali.
We define the singular Hecke algebra as the quotient of the singular braid monoid algebra by the Hecke relations , . We define the notion of Markov trace in this context, fixing the number of singular points, and we prove that a Markov trace determines an invariant on the links with singular points which satisfies some skein relation. Let denote the set of Markov traces with singular points. This is a -vector space. Our main result is that is of dimension . This result is completed...
On montre que les composantes irréductibles du lieu singulier d’une variété de Schubert dans associée à une permutation covexillaire, sont paramétrées par certains des points coessentiels du graphe de la permutation. On donne une description explicite de ces composantes et l’on décrit la singularité le long de chacune d’entre elles.