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- W2769451856 abstract "We introduce a non-symmetric operad $mathcal{N}$, whose dimension in degree $n$ is given by the Catalan number $c_{n-1}$. It arises naturally in the study of coalgebra structures defined on compatible associative algebras. We prove that any free compatible associative algebra admits a compatible infinitesimal bialgebra structure, whose subspace of primitive elements is a $mathcal{N}$-algebra. The data $({rm As},{rm As}^2, mathcal{N})$ is a good triple of operads, in J.-L. Loday's sense. Our construction induces another triple of operads $({rm As},{rm As}_2,{rm As})$, where ${rm As}_2$ is the operad of matching dialgebras. Motivated by A. Goncharov's Hopf algebra of paths $P(S)$, we introduce the notion of bi-matching dialgebras and show that the Hopf algebra $P(S)$ is a bi-matching dialgebras." @default.
- W2769451856 created "2017-12-04" @default.
- W2769451856 creator A5042352967 @default.
- W2769451856 date "2017-11-11" @default.
- W2769451856 modified "2023-09-27" @default.
- W2769451856 title "Compatible associative bialgebras" @default.
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