Finite-dimensional Hopf algebras are free over grouplike subalgebras

DOI10.1016/0022-4049(89)90121-7zbMath0659.16006OpenAlexW2028195665MaRDI QIDQ1112147

M. Bettina Zoeller, Warren D. Nichols

Publication date: 1989

Published in: Journal of Pure and Applied Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0022-4049(89)90121-7

zbMATH Keywords

free modulesimple subcoalgebrasHopf subalgebrafinite-dimensional Hopf algebragroup of group-like elements

Mathematics Subject Classification ID

Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.) (16S10) Group rings (16S34)

Related Items

Unnamed Item, Freeness of infinite dimentional hopf algebras, Divisibility relations for the dimensions and Hilbert series of Nichols algebras of non-Abelian group type., On square roots of the Haar state on compact quantum groups, Freeness of infinite dimensional hopf algebras over grouplike subalgebras, Hopf group-coalgebras

Cites Work

• On blocks of twisted group algebras
• Freeness of Hopf algebras over semisimple group-like subalgebras
• Relative Hopf modules - equivalences and freeness criteria
• Pointed Hopf algebras are free over Hopf subalgebras
• Freeness (projectivity) criteria for Hopf algebras over Hopf subalgebras
• The Order of the Antipode of a Finite Dimensional Hopf Algebra is Finite
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