Comparison of Hopf algebras on trees

By Ralf Holtkamp. 2003

118 citations recorded by the source corpus.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/c9ba3f0b47cc4b39764ec0c9beb4645327c31549

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Algebra and Number Theory

In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Structure of the Loday–Ronco Hopf algebra of trees (2004, methodology): “The obvious importance of these algebras led to intense study, and by work of Foissy [10, 11], Hivert-Novelli-Thibon [16], Holtkamp [19], and Van der Laan [38], the Hopf algebras of Loday-Ronco, Brouder-Frabetti, and the non-commutative Connes-Kreimer Hopf algebra are known to be isomorphic, self-du”
Combinatorial Hopf algebras (2008, background): “Various basis of Dend(K) and comparison between them have been studied in [2, 18, 27].”
Rota–Baxter algebras and dendriform algebras (2005, methodology): “in 1995 with motivation from algebraic K-theory, and was further studied in connection with several areas in mathematics and physics, including operads [54], homology [34, 35], Hopf algebras [13, 47, 58, 65, 32], Lie and Leibniz algebras [35], combinatorics [6, 7, 33, 57], arithmetic [55] and quantu”
On products and duality of binary, quadratic, regular operads (2004, background): “In the next few years, their properties were studied by several authors in areas related to operads [35], homology [17, 18], Hopf algebras [7, 26, 42, 39], combinatorics [16, 37, 2, 3], arithmetic [34] and quantum field theory [16].”
Cocommutative Hopf Algebras of Permutations and Trees (2004, background): “This Hopf algebra also arises as the universal enveloping algebra of the free preLie algebra on one generator, viewed as a Lie algebra [4].”
Bidendriform bialgebras, trees, and free quasi-symmetric functions (2005, background): “3 Free dendriform algebras Let us recall here the construction of the Connes-Kreimer Hopf algebra of planar decorated rooted trees (See [7, 8, 9] for more details).”
Generalized bialgebras and triples of operads (2006, background): “for instance [73, 54, 42, 34, 35, 8, 18], the first step of the proof of the rigidity theorem consists always in writing down such an explicit idempotent.”
FREE ROTA–BAXTER ALGEBRAS AND ROOTED TREES (2005, unknown): “For any y, y′, y′′ ∈ R, if all the triples (y, y′, y′′), (⌊y⌋R, y ′, y′′), (y, ⌊y′⌋R, y ′′), (y, y′, ⌊y′′⌋R), (⌊y⌋R, y ′, ⌊y′′⌋R),(14) (⌊y⌋R, ⌊y ′⌋R, y ′′), (y, ⌊y′⌋R, ⌊y ′′⌋R)(15) are associative triples for ·, then (⌊y⌋R, ⌊y ′⌋R, ⌊y ′′⌋R) is an associative triple for ·.”