Quantum quasi-shuffle algebras II

Jian, Run-Qiang

doi:10.1016/j.jalgebra.2016.10.024

Cited by 4 publications

(1 citation statement)

References 23 publications

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“…They are constructed as a special case of quantum multibrace algebras ( [11]) and have some interesting properties and applications to other mathematical objects (cf. [9], [10], [12]). We can extend the results about quantum quasi-shuffle algebras to the cofree Hopf algebras on Hopf bimodule algebras.…”

Section: Introductionmentioning

confidence: 99%

Cofree Hopf algebras on Hopf bimodule algebras

Fang

Jian

2015

Journal of Pure and Applied Algebra

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Abstract. We investigate a Hopf algebra structure on the cotensor coalgebra associated to a Hopf bimodule algebra which contains universal version of Clifford algebras and quantum groups as examples. It is shown to be the bosonization of the quantum quasi-shuffle algebra built on the space of its right coinvariants. The universal property and a Rota-Baxter algebra structure are established on this new algebra.

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Section: Introductionmentioning

confidence: 99%

Cofree Hopf algebras on Hopf bimodule algebras

Fang

Jian

2015

Journal of Pure and Applied Algebra

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Coherent unit actions on braided operads and Hopf algebras

Guo

2021

Contemporary Mathematics

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

Guo

2021

J. Algebra Appl.

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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 algebra 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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Quantum quasi-shuffle algebras II

Cited by 4 publications

References 23 publications

Cofree Hopf algebras on Hopf bimodule algebras

Cofree Hopf algebras on Hopf bimodule algebras

Coherent unit actions on braided operads and Hopf algebras

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

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