Tridendriform Structures

IF 0.9 3区物理与天体物理 Q2 MATHEMATICS

Symmetry Integrability and Geometry-Methods and Applications Pub Date : 2023-09-15 DOI:10.3842/sigma.2023.066

Pierre Catoire

引用次数: 0

Abstract

Inspired by the work of J-L. Loday and M. Ronco, we build free tridendriform algebras over reduced trees and we show that they have a coproduct satisfying some compatibilities with the tridendriform products. Its graded dual is the opposite bialgebra of TSym introduced by N. Bergeron et al., which is described by the lightening splitting of a tree. In particular, we can split the product in three pieces and the coproduct in two pieces with Hopf compatibilities. We generate its codendriform primitives and count its coassociative primitives thanks to L. Foissy's work.

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Tridendriform结构

受到J-L作品的启发。Loday和M. Ronco，我们在约简树上建立了自由的三叉形代数我们证明了它们有一个与三叉形乘积相容的副积。它的梯度对偶是N. Bergeron等人引入的TSym的相反双代数，用树的闪电分裂来描述。特别地，我们可以将乘积分成三块，副乘积分成两块，并具有Hopf兼容性。由于L. Foissy的工作，我们生成了它的共树形原语并计算了它的协联想原语。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Symmetry Integrability and Geometry-Methods and Applications 物理-物理：数学物理

CiteScore

1.80

自引率

0.00%

发文量

审稿时长

4-8 weeks

期刊介绍： Scope Geometrical methods in mathematical physics Lie theory and differential equations Classical and quantum integrable systems Algebraic methods in dynamical systems and chaos Exactly and quasi-exactly solvable models Lie groups and algebras, representation theory Orthogonal polynomials and special functions Integrable probability and stochastic processes Quantum algebras, quantum groups and their representations Symplectic, Poisson and noncommutative geometry Algebraic geometry and its applications Quantum field theories and string/gauge theories Statistical physics and condensed matter physics Quantum gravity and cosmology.