The set of types of \(n\)-dimensional semisimple and cosemisimple Hopf algebras is finite

DOI10.1006/jabr.1996.6991zbMath0882.16029OpenAlexW2014098065MaRDI QIDQ1364304

Dragoş Ştefan

Publication date: 4 March 1998

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

Full work available at URL: https://doi.org/10.1006/jabr.1996.6991

zbMATH Keywords

cohomologynumbers of orbitsHopf modulesYetter-Drinfeld modulesDrinfeld double\(n\)-dimensional bialgebras\(n\)-dimensional semisimple cosemisimple Hopf algebrasbialgebra structures on \(n\)-dimensional vector spaces

Mathematics Subject Classification ID

Related Items (21)

Semisimple weak Hopf algebras. ⋮ DEFORMATION COHOMOLOGY FOR YETTER-DRINFEL'D MODULES AND HOPF (BI)MODUL ES ⋮ Bialgebra Cohomology of the Duals of a Class of Generalized Taft Algebras ⋮ On faithfulness of the lifting for Hopf algebras and fusion categories ⋮ Semisimple Hopf algebras via geometric invariant theory ⋮ GROWTH ESTIMATES FOR DISCRETE QUANTUM GROUPS ⋮ Every central simple algebra is Brauer equivalent to a Hopf Schur algebra. ⋮ The Frucht property in the quantum group setting ⋮ Compact semisimple 2-categories ⋮ On the classification of finite-dimensional semisimple Hopf algebras ⋮ Categorical Morita equivalence and monoidal Morita equivalence of semisimple Hopf algebras of dimension pqr ⋮ Finiteness of the number of coideal subalgebras ⋮ On Hopf algebras with positive bases ⋮ Degeneration, Rigidity and Irreducible Components of Hopf algebras ⋮ Classification of Semisimple Hopf Algebras ⋮ Hopf Algebras ⋮ On Kaplansky's fifth conjecture ⋮ Lifting of quantum linear spaces and pointed Hopf algebras of order \(p^3\) ⋮ Nonsemisimple Hopf algebras of dimension 8𝑝 with the Chevalley property ⋮ A survey of Hopf algebras of low dimension. ⋮ On the structure of weak Hopf algebras

Cites Work

• Finite dimensional cosemisimple Hopf algebras in characteristic 0 are semisimple
• Hopf modules and Yetter-Drinfel'd modules
• Bialgebra cohomology, deformations, and quantum groups.
• The Group of Automorphisms of a Semisimple Hopf Algebra Over a Field of Characteristic 0 is Finite
• Algebras and their automorphism groups
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