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- W3105196268 abstract "Motivated by the classical comatrix coalgebra, we introduce the concept of a Newtonian comatrix coalgebra. We construct an infinitesimal unitary bialgebra on a matrix algebra and a weighted infinitesimal unitary bialgebra on a non-commutative polynomial algebra, via two constructions of suitable coproducts. As a consequence, a Newtonian comatrix coalgebra is established. Furthermore, an infinitesimal unitary Hopf algebra, under the view of Aguiar, is constructed on a matrix algebra. By investigating the relationship between weighted infinitesimal bialgebras and pre-Lie algebras, we erect respectively a pre-Lie algebraic structure and further a new Lie algebraic structure on matrix algebras. Finally, a pre-Lie algebraic structure and a Lie algebraic structure on non-commutative polynomial algebras are also given." @default.
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- W3105196268 date "2019-05-16" @default.
- W3105196268 modified "2023-09-27" @default.
- W3105196268 title "Weighted infinitesimal unitary bialgebras, pre-Lie, matrix algebras, and polynomial algebras" @default.
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- W3105196268 doi "https://doi.org/10.1080/00927872.2019.1612422" @default.
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