Typed angularly decorated planar rooted trees and generalized Rota-Baxter algebras

DOI10.1007/S10801-022-01168-5zbMath1517.17016arXiv2112.02859MaRDI QIDQ6384888

Publication date: 6 December 2021

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 $Omega$ 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 $lambda$-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 $Omega$-Rota-Baxter algebras generated by a commutative algebra A in terms of typed words.

Mathematics Subject Classification ID

Trees (05C05) Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.) (16S10) Free algebras (08B20) Yang-Baxter equations and Rota-Baxter operators (17B38)

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