Dendriform Equations
arXiv:0805.0762 · doi:10.1016/j.jalgebra.2009.06.002
Abstract
We investigate solutions for a particular class of linear equations in dendriform algebras. Motivations as well as several applications are provided. The latter follow naturally from the intimate link between dendriform algebras and Rota-Baxter operators, e.g. the Riemann integral or Jackson's q-integral.
improved version
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Cited by in corpus (13)
- Two interacting Hopf algebras of trees
- Cumulants, free cumulants and half-shuffles
- Twisted dendriform algebras and the pre-Lie Magnus expansion
- Monotone, free, and boolean cumulants: a shuffle algebra approach
- Time-ordering and a generalized Magnus expansion
- Pluriassociative algebras II: The polydendriform operad and related operads
- The combinatorics of Green's functions in planar field theories
- Shuffle group laws. Applications in free probability
- Dual immaculate creation operators and a dendriform algebra structure on the quasisymmetric functions
- Cumulant-cumulant relations in free probability theory from Magnus' expansion
- The tridendriform structure of a Magnus expansion
- Evaluating Generating Functions for Periodic Multiple Polylogarithms
- Conditionally monotone cumulants via shuffle algebra