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arXiv · 2112.07981

Reduced typed angularly decorated planar rooted trees and generalized tridendriform algebras

Loïc Foissy·Xiao-Song Peng
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Abstract

We introduce a generalization of tridendriform algebras, where each of the three products are replaced by a family of products indexed by a set $\Omega$. We study the needed structure on $\Omega$ for free $\Omega$-tridendriform algebras to be built on Schr{\"o}der trees (as it is the case in the classical case), with convenient decorations on their leaves. We obtain in this way extended triassociative semigroups. We describe commutative $\Omega$-tridendriform algebras in terms of typed words. We also study links with generalizations of Rota-Baxter algebras and describe the Koszul duals of the corresponding operads.

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Loïc Foissy, Xiao-Song Peng. 2021-12-15. Reduced typed angularly decorated planar rooted trees and generalized tridendriform algebras. https://arxiv.org/abs/2112.07981

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