Letters in Mathematical Physics

, Volume 92, Issue 1, pp 1–16 | Cite as

Quantum Quasi-Shuffle Algebras

  • Run-Qiang Jian
  • Marc Rosso
  • Jiao Zhang


We establish some properties of quantum quasi-shuffle algebras. They include the necessary and sufficient condition for the construction of the quantum quasi-shuffle product, the universal property, and the commutativity condition. As an application, we use the quantum quasi-shuffle product to construct a linear basis of T(V), for a special kind of Yang–Baxter algebras (V, m, σ).

Mathematics Subject Classification (2010)

16T25 17B37 


quantum quasi-shuffle algebra connected twisted Yang–Baxter bialgebra Lyndon word 


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Copyright information

© Springer 2010

Authors and Affiliations

  1. 1.School of Computer ScienceDongguan University of TechnologyDongguanPeople’s Republic of China
  2. 2.Institut de Mathématiques de JussieuUniversité Paris Diderot (Paris 7)ParisFrance
  3. 3.Department of MathematicsSun Yat-sen UniversityGuangzhouPeople’s Republic of China
  4. 4.Department of MathematicsEast China Normal UniversityShanghaiPeople’s Republic of China

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