Nijenhuis algebras, NS algebras, and N-dendriform algebras

New Identities in Dendriform Algebras

Dendriform structures arise naturally in algebraic combinatorics (where they allow, for example, the splitting of the shuffle product into two pieces) and through Rota–Baxter algebra structures (the latter appear, among others, in differential systems and in the renormalization process of pQFT). We prove new combinatorial identities in dendriform dialgebras that appear to be strongly related to...

Infinitesimal Bialgebras, Pre-lie and Dendriform Algebras

We introduce the categories of infinitesimal Hopf modules and bimodules over an infinitesimal bialgebra. We show that they correspond to modules and bimodules over the infinitesimal version of the double. We show that there is a natural, but non-obvious way to construct a pre-Lie algebra from an arbitrary infinitesimal bialgebra and a dendriform algebra from a quasitriangular infinitesimal bial...

On Heyting algebras and dual BCK-algebras

A Heyting algebra is a distributive lattice with implication and a dual $BCK$-algebra is an algebraic system having as models logical systems equipped with implication. The aim of this paper is to investigate the relation of Heyting algebras between dual $BCK$-algebras. We define notions of $i$-invariant and $m$-invariant on dual $BCK$-semilattices and prove that a Heyting semilattice is equiva...

M ar 2 00 5 ROTA - BAXTER ALGEBRAS , DENDRIFORM ALGEBRAS AND POINCARÉ - BIRKHOFF - WITT THEOREM

Rota-Baxter algebras appeared in both the physics and mathematics literature. It is of great interest to have a simple construction of the free object of this algebraic structure. For example, free commutative Rota-Baxter algebras relate to double shuffle relations for multiple zeta values. The interest in the non-commutative setting arised in connection with the work of Connes and Kreimer on t...

Gröbner-Shirshov bases for the non-symmetric operads of dendriform algebras and quadri-algebras