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- W3106080167 abstract "Parallel to operated algebras built on top of planar rooted trees via the grafting operator $B^+$, we introduce and study $vee$-algebras and more generally $vee_Omega$-algebras based on planar binary trees. Involving an analogy of the Hochschild 1-cocycle condition, cocycle $vee_Omega$-bialgebras (resp.~$vee_Omega$-Hopf algebras) are also introduced and their free objects are constructed via decorated planar binary trees. As a special case, the well-known Loday-Ronco Hopf algebra $H_{LR}$ is a free cocycle $vee$-Hopf algebra. By means of admissible cuts, a combinatorial description of the coproduct $Delta_{LR(Omega)}$ on decorated planar binary trees is given, as in the Connes-Kreimer Hopf algebra by admissible cuts." @default.
- W3106080167 created "2020-11-23" @default.
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- W3106080167 date "2019-05-20" @default.
- W3106080167 modified "2023-09-24" @default.
- W3106080167 title "Hopf algebras of planar binary trees: an operated algebra approach" @default.
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- W3106080167 doi "https://doi.org/10.1007/s10801-019-00885-8" @default.
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