Cocommutative vertex bialgebras

Infinitesimal or Cocommutative Dipterous Bialgebras and Good Triples of Operads

The works of Poincaré, Birkhoff, Witt and Cartier, Milnor, Moore on the connected cocommutative Hopf algebras translated in the language of operads means that the triple of operads (Com,As, Lie) endowed with the Hopf compatiblity relation is good. In this paper, we focus on left dipterous (resp. right dipterous) algebras which are associative algebras with an extra left (resp. right) module on ...

Coderivations of Cocommutative Coalgebras

Poisson bialgebras

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Shuffle Bialgebras

The goal of our work is to study the spaces of primitive elements of the Hopf algebras associated to the permutahedra and the associahedra. We introduce the notion of shuffle bialgebras, and compute the subpaces of primitive elements associated to these algebras. These spaces of primitive elements have natural structure of some type of algebras which we describe in terms of generators and relat...

Drinfeld-hecke Algebras over Cocommutative Algebras

If A is a cocommutative algebra with coproduct, then so is the smash product algebra of a symmetric algebra SymV with A, where V is an A-module. Such smash product algebras, with A a group ring or a Lie algebra, have been deformed by Drinfel’d and more recently, Crawley-Boevey and Holland, Etingof and Ginzburg (and Gan), and others. These algebras include symplectic reflection algebras and infi...