Freeness of Hopf algebras over semisimple group-like subalgebras
Let H be a finite-dimensional Hopf algebra over a field k, G(H) its group of group-like elements (i.e., elements \(g\neq 0\) in H with \(\Delta g=g\otimes g)\). Let L be a subgroup of G(H). The author proves that if kL is semisimple, i.e., char k does not divide \(| L|\), then H is free as left kL-module. Use is made of criteria developed by \textit{D. E. Radford} [J. Pure Appl. Algebra 11, 15-28 (1977; Zbl 0367.16004)] for Hopf algebras to be free modules over group-like subalgebras. \{Reviewer's note: W. D. Nichols and the author have recently removed the restriction that kL be semisimple. In fact, they have more recently shown that a finite-dimensional Hopf algebra is a free module over any Hopf subalgebra.\}
free modules over group-like subalgebras
scientific article; zbMATH DE number 4059605