2021/03/01 by Kangqiao Li, Li, Kangqiao · 1 citation
Mathematics · #Algebraic structures and combinatorial models #Advanced Topics in Algebra #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.2103.01298
The link relation on simple subcoalgebras is used for decompositions of coalgebras. In this paper, we provide more sufficient conditions for this link relation, and prove a formula on the products between link-indecomposable components of Hopf algebras with the dual Chevalley property. Furthermore, we show that each of its component is generated by a simple subcoalgebra, as a faithfully flat module (in fact, a projective generator) over a Hopf subalgebra which is the component containing the unit element. Our conclusions generalize some relevant results on pointed Hopf algebras, which were established by Montgomery in 1995.