Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Braided Rota-Baxter algebras, quantum quasi-shuffle algebras and braided
  dendriform algebras   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.

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The categories of this paper are: solv-int
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The categories of this paper are: hep-ph
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The categories of this paper are: eess
3
The categories of this paper are: physics
4
The categories of this paper are: cond-mat
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The categories of this paper are: plasm-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: econ
1
The categories of this paper are: cs
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The categories of this paper are: chao-dyn
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The categories of this paper are: astro-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: supr-con
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The categories of this paper are: q-alg
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The categories of this paper are: acc-phys
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The categories of this paper are: ao-sci