17 citations · 37 across the 7 of their papers we have counts for
7 papers · 1 filter
Planar trees, free nonassociative algebras, invariants, and elliptic integrals
Vesselin Drensky, Ralf Holtkamp
We consider absolutely free nonassociative algebras and, more generally, absolutely free algebras with (maybe infinitely) many multilinear operations. Such algebras are described i…
Partial magmatic bialgebras
Emily Burgunder, Ralf Holtkamp
A partial magmatic bialgebra, (T;S)-magmatic bialgebra where T \subset S are subsets of the set of positive integers, is a vector space endowed with an n-ary operation for each n i…
Coassociative magmatic bialgebras and the Fine numbers
Ralf Holtkamp, Jean-Louis Loday, Maria Ronco
We prove a structure theorem for the connected coassociative magmatic bialgebras. The space of primitive elements is an algebra over an operad called the primitive operad. We prove…
On Hopf algebra structures over free operads
Ralf Holtkamp
The operad Lie can be constructed as the operad of primitives Prim As from the operad As of associative algebras. This is reflected by the theorems of Friedrichs, Poincare'-Birkhof…
On Hopf algebra structures over operads
Ralf Holtkamp
We study P-Hopf algebras with one coassociative cooperation over different operads P. For example, we consider the Loday-Ronco dendriform Hopf algebra and its isomorphisms with the…
Constants of formal derivatives of non-associative algebras, Taylor expansions and applications
Vesselin Drensky, Ralf Holtkamp
We study unitary multigraded non-associative algebras R generated by an ordered set X over a field K of characteristic 0 such that the mappings d_k: x_l->delta_{kl}, x_k,x_l in X,…