Braided Rota-Baxter algebras, quantum quasi-shuffle algebras and braided dendriform algebras

Abstract

Rota-Baxter algebras and the closely related dendriform algebras have important physics applications, especially to renormalization of quantum field theory. Braided structures provide effective ways of quantization such as for quantum groups. Continuing recent study relating the two structures, this paper considers Rota-Baxter algebras and dendriform algebras in the braided contexts. Applying the quantum shuffle and quantum quasi-shuffle products, we construct free objects in the categories of braided Rota-Baxter algebras and braided dendriform algebras, under the commutativity condition. We further generalize the notion of dendriform Hopf algebras to the braided context and show that quantum shuffle algebra gives a braided dendriform Hopf algebra. Enveloping braided commutative Rota-Baxter algebras of braided commutative dendriform algebras are obtained.

arXiv comment20 pages

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Cited by in corpus (3)

• Representations and Modules of Rota-Baxter Algebras
• Braided dendriform and tridendriform algebras and braided Hopf algebras of planar trees
• Coherent unit actions on braided operads and Hopf algebras