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arXiv · 1812.02319

Weighted infinitesimal unitary bialgebras, pre-Lie, matrix algebras and polynomial algebras

Yi Zhang·Jiawen Zheng·Yanfeng Luo
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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.

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Yi Zhang, Jiawen Zheng, Yanfeng Luo. 2018-12-05. Weighted infinitesimal unitary bialgebras, pre-Lie, matrix algebras and polynomial algebras. https://doi.org/10.1080/00927872.2019.1612422

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