A Quantization of the Loday-Ronco Hopf Algebra

• DOI: 10.48550/arxiv.2109.09680
• Publication Date: 2021-01-01
• Authors: João N. Esteves
• Keywords: 05C10, 05C25, 16T05 (Primary) 81R10, 81R50, 81T32 (Secondary); Mathematics - Quantum Algebra; FOS: Mathematics; Mathematics - Combinatorics; Quantum Algebra (math.QA); FOS: Physical sciences; Mathematical Physics (math-ph); Combinatorics (math.CO); 0101 mathematics; 01 natural sciences; Mathematical Physics

We propose a quantization algebra of the Loday-Ronco Hopf $k[Y^\infty]$, based on Topological Recursion formula Eynard and Orantin. have shown in previous works that planar binary trees is space solutions for genus 0 version Recursion, an extension Loday Ronco as to include some new graphs with loops correct setting find solution arbitrary genus. Here we show this $k[Y^\infty]_h$ still can be seen sense made precise text trees, $\mathcal{A}^h_{\text{TopRec}}$ subalgebra quotient $\mathcal{A}_{\text{Reg}}^h$ obtained from nevertheless doesn't inherit structure. end paper discussion cohomology low degree.