Infinite magmatic bialgebras
Copyright policy )Infinite magmatic bialgebras
An infinite magmatic bialgebra is a vector space endowed with an n-ary operation, and an n-ary cooperation, for each n, verifying some compatibility relations. We prove a rigidity theorem, analogue to the Hopf-Borel theorem for commutative bialgebras: any connected infinite magmatic bialgebra is of the form $Mag^\infty(Prim H)$, where $Mag^\infty(V)$ is the free infinite magmatic algebra over the vector space V.
- University of Montpellier France
Other \(n\)-ary compositions \((n \ge 3)\), Applied Mathematics, Connections of Hopf algebras with combinatorics, 17Axx, Mathematics - Rings and Algebras, planar binary trees, Bialgebra, Hopf algebra, Trees, magmatic bialgebras, operads, Bialgebras, Hopf algebras, 18D50, Rings and Algebras (math.RA), Cartier–Milnor–Moore, \(n\)-ary operations, 17A50, FOS: Mathematics, Operads, Operad, Poincaré–Birkhoff–Witt, 17A50; 18D50; 17Axx
Other \(n\)-ary compositions \((n \ge 3)\), Applied Mathematics, Connections of Hopf algebras with combinatorics, 17Axx, Mathematics - Rings and Algebras, planar binary trees, Bialgebra, Hopf algebra, Trees, magmatic bialgebras, operads, Bialgebras, Hopf algebras, 18D50, Rings and Algebras (math.RA), Cartier–Milnor–Moore, \(n\)-ary operations, 17A50, FOS: Mathematics, Operads, Operad, Poincaré–Birkhoff–Witt, 17A50; 18D50; 17Axx
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