TY - JOUR
T1 - Mixable shuffles, quasi-shuffles and Hopf algebras
AU - Ebrahimi-Fard, Kurusch
AU - Guo, Li
N1 - Funding Information:
Acknowledgements We thank Zongzhu Lin and James Stasheff for helpful discussions and thank the referee for detailed comments that improved the clarity of the presentation. The first named author thanks the I.H.É.S. for warm hospitality, and the Ev. Studienwerk for financial support. The second named author acknowledges support from NSF grant DMS 0505643 and hospitality from the MPI for Mathematics at Bonn where the revision was completed.
PY - 2006/8
Y1 - 2006/8
N2 - The quasi-shuffle product and mixable shuffle product are both generalizations of the shuffle product and have both been studied quite extensively recently. We relate these two generalizations and realize quasi-shuffle product algebras as subalgebras of mixable shuffle product algebras. As an application, we obtain Hopf algebra structures in free Rota-Baxter algebras.
AB - The quasi-shuffle product and mixable shuffle product are both generalizations of the shuffle product and have both been studied quite extensively recently. We relate these two generalizations and realize quasi-shuffle product algebras as subalgebras of mixable shuffle product algebras. As an application, we obtain Hopf algebra structures in free Rota-Baxter algebras.
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U2 - 10.1007/s10801-006-9103-x
DO - 10.1007/s10801-006-9103-x
M3 - Article
AN - SCOPUS:33745726181
SN - 0925-9899
VL - 24
SP - 83
EP - 101
JO - Journal of Algebraic Combinatorics
JF - Journal of Algebraic Combinatorics
IS - 1
ER -