On the Associative Analog of Lie Bialgebras

By Marcelo Aguiar. 2001

246 citations recorded by the source corpus.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/8811f41ad48b393a1529a4724dfb54e527a32705

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In Algebra and Number Theory

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In Mathematical Physics

Citations in the corpus

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.”
Infinitesimal bialgebras, pre-Lie and dendriform algebras (2002, methodology): “Infinitesimal bialgebras were introduced by Joni and Rota [17, Section XII].”
Operated semigroups, Motzkin paths and rooted trees (2007, unknown): “Given the recent progresses on Rota-Baxter algebra in both theoretical and application aspects [1, 2, 10, 16, 17, 19, 20, 26, 27, 29, 30, 31], it is desirable to obtain convenient constructions of free Rota-Baxter algebras.”
Matching Rota-Baxter algebras, matching dendriform algebras and matching pre-Lie algebras (2019, methodology): “For the classical case of one linear operator, see [2, 16] Theorem 3.”
On Differential Rota-Baxter Algebras (2007, methodology): “Likewise, the integral operator P and summation operator have been abstracted to give the notion of Rota-Baxter operators (previously called Baxter operators) and Rota-Baxter algebras [3, 25, 26].”
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”
Deformations of associative Rota-Baxter operators (2019, methodology): “The notion of infinitesimal bialgebra was introduced by Aguiar as an associative analog of Lie bialgebras [1,3].”
NEW IDENTITIES IN DENDRIFORM ALGEBRAS (2007, background): “Aguiar established in [Agu02] unexpected connections with the infinitesimal bialgebra structures studied in [Agu99, Agu01 ].”