Freeness of infinite dimentional hopf algebras

DOI10.1080/00927879208824415zbMath0804.16042OpenAlexW2174603878MaRDI QIDQ4005848

Warren D. Nichols, M. Bettina Richmond

Publication date: 27 September 1992

Published in: Communications in Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/00927879208824415

zbMATH Keywords

Hopf algebrasHopf subalgebrasinfinite dimensional Hopf algebrasfinite dimensional semisimple Hopf subalgebrasfree \(B\)-modules

Mathematics Subject Classification ID

Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.) (16S10) Free, projective, and flat modules and ideals in associative algebras (16D40) Structure and classification for modules, bimodules and ideals (except as in 16Gxx), direct sum decomposition and cancellation in associative algebras) (16D70)

Related Items

Noetherian PI Hopf algebras are Gorenstein, Unnamed Item, Enveloping algebras that are principal ideal rings, PBW-bases of coideal subalgebras and a freeness theorem, A Hopf Algebra Freeness Result Revisited, Some remarks on exact sequences of quantum groups

Cites Work

• Freeness of Hopf algebras over semisimple group-like subalgebras
• Finite-dimensional Hopf algebras are free over grouplike subalgebras
• Relative Hopf modules - equivalences and freeness criteria
• Untergruppen formeller Gruppen von endlichem Index
• Pointed Hopf algebras are free over Hopf subalgebras
• Freeness (projectivity) criteria for Hopf algebras over Hopf subalgebras
• Freeness of infinite dimensional hopf algebras over grouplike subalgebras
• A Hopf Algebra Freeness Theorem