Baxter Algebras and Hopf Algebras

By George E. Andrews, Li Guo, William F. Keigher, Ken Ichi Ono. 2003

70 citations recorded by the source corpus.

By applying a recent construction of free Baxter algebras, we obtain a new class of Hopf algebras that generalizes the classical divided power Hopf algebra. We also study conditions under which these Hopf algebras are isomorphic.

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Citations in the corpus

On products and duality of binary, quadratic, regular operads (2004, background): “…largely inspired by the connection [1, 10, 27] with Rota-Baxter operators1 which were introduced by G. Baxter [6] in 1960 and were actively studied in the 1970s [43, 44] and again in recent years in connection with several areas of mathematics and physics [5, 8, 9, 11, 12, 15, 15, 23, 24, 21, 22,…”
Mixable shuffles, quasi-shuffles and Hopf algebras (2005, methodology): “In recent years, Rota-Baxter algebras have found applications in quantum field theory [8, 9, 15, 16, 17], dendriform algebras [1, 10, 13, 31], number theory [22], Hopf algebras [2] and combinatorics [21].”
Embedding of dendriform algebras into Rota-Baxter algebras (2011, background): “me, numerous connections of Rota—Baxter operators with other areas of mathematics are found. The latter include quantum ﬁeld theory, Young—Baxter equations, operads, Hopf algebras, number theory etc. [2, 13, 14, 16, 24]. The notion of a Leibniz algebra introduced by J.-L. Loday [25] is originated fr”
Renormalization of multiple zeta values (2006, methodology): “mixable shuﬄe arises from the construction of free commutative Rota–Baxter algebras and has been denoted by ⋄+ in the literature of Rota–Baxter algebras (previously known as Baxter algebras), such as [4, 17, 18, 19, 27, 28, 29, 30, 31]. We adapt the notation ∗ to be consistent with the current conve”
Rota–Baxter algebras and dendriform algebras (2005, background): “Recently, there have been several interesting developments of Rota-Baxter algebras in theoretical physics and mathematics, including quantum field theory [14, 15], Yang-Baxter equations [1, 2, 3], shuffle products [19, 41, 42], operads [4, 16, 20, 50, 51, 52], Hopf algebras [8, 19, 31], combinatoric”
FREE ROTA–BAXTER ALGEBRAS AND ROOTED TREES (2005, methodology): “In fact, such a relation for Lie algebras was introduced independently by Belavin and Drinfeld [8], and Semenov-Tian-Shansky [58] in the 1980s, under the disguise of r-matrices, of the (modified) classical Yang–Baxter equation, named after the physicists Chen-ning Yang and Rodney Baxter.”