|
Speaker:
J.-L. Loday, CNRS, Strasbourg
Title:
Generalized bialgebras and triples of operads
Abstract:
For connected cocommutative Hopf algebras there is a
structure theorem which says that they are cofree (PBW) and that they
are all universal enveloping algebras of their primitive part,
considered as a Lie algebra(CMM). What happens when we drop the
cocommutative hypothesis? We will give an answer to this question and
show that it leads to the search of "triples of operads" (C,A,P) where
C is for the coalgebra structure, A for the algebra structure, and P
for the primitive part structure. The case (Com,As,Lie) being the
classical case referred to above. Several instances of triples of
operads come from combinatorial questions.
|