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- W4200632783 abstract "We introduce a generalization of parametrized Rota–Baxter algebras, named $$Omega $$ -Rota–Baxter algebra, 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 $$Omega $$ -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." @default.
- W4200632783 created "2021-12-31" @default.
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- W4200632783 date "2022-09-14" @default.
- W4200632783 modified "2023-10-04" @default.
- W4200632783 title "Typed angularly decorated planar rooted trees and generalized Rota–Baxter algebras" @default.
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- W4200632783 doi "https://doi.org/10.1007/s10801-022-01168-5" @default.
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