On the Associative Analog of Lie Bialgebras

2001/10/01 by Marcelo Aguiar · 25 citations
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Advanced Operator Algebra Research

paper · doi:10.1006/jabr.2001.8877

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• Dualite de Koszul des PROPs
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• Commutative modified Rota-Baxter algebras, shuffle products and Hopf algebras
• Hom-coassociative ternary coalgebras and infinitesimal bialgebras
• (Co)associative 3-ary (co)algebras and infinitesimal bialgebras:\n construction and main properties
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• Structure theorems of mixable shuffle algebras and free commutative Rota-Baxter algebras
• Cocycle weighted infinitesimal bialgebras and pre-Lie algebras on rooted trees
• Twisting on associative algebras and Rota-Baxter type operators
• A further study on averaging commutative and cocommutative infinitesimal bialgebras and special apre-perm bialgebras
• ω-Lie bialgebras and ω-Yang-Baxter equation
• Bi-Hamiltonian ODEs with matrix variables
• Anti-Frobenius Algebras and Associative Yang-Baxter Equation
• R-matrix Dunkl operators and spin Calogero-Moser system
• Anti-pre-Poisson bialgebras and relative Rota-Baxter operators
• A new approach to the bialgebra theory for relative Poisson algebras
• Infinitesimal bialgebras, pre-Lie and dendriform algebras
• Trigonometric solutions of the associative Yang-Baxter equation
• Induced structures of averaging commutative and cocommutative infinitesimal bialgebras via a new splitting of perm algebras
• Matching Hom-Setting of Rota-Baxter algebras, dendriform algebras and pre-Lie algebras
• Operator forms of nonhomogeneous associative classical Yang-Baxter equation
• Double constructions of Heisenberg Frobenius algebras and Connes\n cocycles, and solutions of the three-dimensional associative Yang-Baxter\n equation
• Weighted infinitesimal unitary bialgebras on matrix algebras and weighted associative Yang-Baxter equations