Loday-type Algebras and the Rota-Baxter Relation

Abstract

In this brief note we would like to report on an observation concerning the relation between Rota-Baxter operators and Loday-type algebras, i.e. dendriform di- and trialgebras. It is shown that associative algebras equipped with a Rota-Baxter operator of arbitrary weight always give such dendriform structures.

13 pages, no figures, short remark at the end of Sect. 4 added, minor typos corrected

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• Renormalization in quantum field theory and the Riemann-Hilbert problem I: the Hopf algebra structure of graphs and the main theorem
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• On some remarkable operads constructed from Baxter operators
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• Rota-Baxter Operators on Quadratic Algebras
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• The combinatorics of Bogoliubov's recursion in renormalization
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• Left-symmetric Superalgebra Structures on the Super-Virasoro Algebras
• Cohomology of weighted Rota-Baxter Lie algebras and Rota-Baxter paired operators
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