TYPED ANGULARLY DECORATED PLANAR ROOTED TREES AND GENERALIZED ROTA-BAXTER ALGEBRAS - Archive ouverte HAL Access content directly
Preprints, Working Papers, ... Year : 2022

TYPED ANGULARLY DECORATED PLANAR ROOTED TREES AND GENERALIZED ROTA-BAXTER ALGEBRAS

Abstract

We introduce a generalization of parametrized Rota-Baxter algebras, which includes family and matching Rota-Baxter algebras. We study the structure needed on the set Ω of parameters in order to obtain that free Rota-Baxter algebras are described in terms of typed and angularly decorated planar rooted trees: we obtain the notion of λ-extended diassociative semigroup, which includes sets (for matching Rota-Baxter algebras) and semigroups (for family Rota-Baxter algebras), and many other examples. We also describe free commutative Ω-Rota-Baxter algebras generated by a commutative algebra A in terms of typed words.
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Dates and versions

hal-03464744 , version 1 (03-12-2021)
hal-03464744 , version 2 (11-05-2022)

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Loïc Foissy, Xiao-Song Peng. TYPED ANGULARLY DECORATED PLANAR ROOTED TREES AND GENERALIZED ROTA-BAXTER ALGEBRAS. 2022. ⟨hal-03464744v2⟩
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