Lie Theory for Hopf operads

The map κ from signed per- mutations to Cambrian trees is known to encode combinatorial and geometric properties of the Cambrian structures: the Cambrian lattice is the quotient of

This Lie algebra is therefore free, and its quotient is A/(a). This proves the theorem.. Under the hypothesis of Theorem 2, we show that d 2 = 0 and that the spectral

We study the h -trivial deformations of the standard embedding of the Lie algebra Vect( S 1 ) of smooth vector fields on the circle, into the Lie algebra of functions on the

After reviewing the definition of the restricted quantum group U q sℓ(2), we give our quasi-Hopf algebra modification U (Φ) q sℓ(2), and we show that it is indeed a factorisable

When the normal subgroupoid S in the locally compact twisted groupoid extension with Haar systems (G, Σ, S) is abelian and the restriction Σ |S of the twist is also abelian, one can

A further non-commutative Hopf algebra of TAGs can be defined when considering only graphs of a given quantum field theoretical model and defin- ing the coproduct as the appropriate

The study of this dendriform structure is postponed to the appendix, as well as the enumeration of partitioned trees; we also prove that free Com-Prelie algebras are free as

The Connes-Kreimer Hopf algebra of rooted trees, introduced in [1, 6, 7, 8], is a commutative, non cocommutative Hopf algebra, its coproduct being given by admissible cuts of trees2.