Compatible associative products and trees

By Vladimir Dotsenko. 2008

73 citations recorded by the source corpus.

We compute dimensions of graded components for free algebras with two compatible associative products, and give a combinatorial interpretation of these algebras in terms of planar rooted trees.

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

View Paper: https://www.semanticscholar.org/paper/2938833c4a6d80b7d1528470c6af83975efbdcbc

Citations in the corpus

• On the operad of associative algebras with derivation (2009, unknown): “The relations are: { µ ◦ (µ, id) = µ ◦ (id, µ), D ◦ µ = µ ◦ (D, id) + µ ◦ (id, D).”
• Encyclopedia of types of algebras 2010 (2010, unknown): “ Koszul. Alternative Relationship (Ash2i)!-alg→ As(2)-alg→ Ash2i-alg Unit Comment equivalently λ x∗ y +µ x·y is associative for any λ,µ Variations: Ashki, Hoch-alg. Ref. for instance [Gon05], [OS06], [Dot09]. 40 G.W.ZINBIEL Name L-dendriform algebra Notation L-dend Def. oper. x ⊲ y and x ⊳ y sym. re”