Finiteness conditions for a Hopf algebra with a nonzero integral

DOI10.1016/0021-8693(77)90400-8zbMath0361.16002OpenAlexW2038400273MaRDI QIDQ1239359

David E. Radford

Publication date: 1977

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

Full work available at URL: https://doi.org/10.1016/0021-8693(77)90400-8

Mathematics Subject Classification ID

Related Items (27)

Symmetric coalgebras. ⋮ Generalized smash products. ⋮ The antipode of a dual quasi-Hopf algebra with nonzero integrals is bijective. ⋮ Integrals, quantum Galois extensions, and the affineness criterion for quantum Yetter-Drinfel'd modules ⋮ New results on the bijectivity of antipode of a Hopf algebra. ⋮ Uncertainty inequalities for hopf algebras ⋮ Radford's \(S^4\) formula for co-Frobenius Hopf algebras. ⋮ Galois extensions for co-Frobenius Hopf algebras ⋮ Finiteness conditions, co-Frobenius Hopf algebras, and quantum groups ⋮ The Bijectivity of the Antipode Revisited ⋮ Integrals for (dual) quasi-Hopf algebras. Applications ⋮ Twisted tensor product of multiplier Hopf (*-)algebras. ⋮ Semiartinian profinite algebras have nilpotent Jacobson radical. ⋮ A generalized Frobenius structure for coalgebras with applications to character theory ⋮ The Drinfel'd double of multiplier Hopf algebras. ⋮ NOETHERIAN HOPF ALGEBRAS ⋮ On the flatness and the projectivity over Hopf subalgebras of Hopf algebras over Dedekind rings ⋮ A-H-BIMODULES AND EQUIVALENCES ⋮ Monadic cointegrals and applications to quasi-Hopf algebras ⋮ Splitting comodules over Hopf algebras and application to representation theory of quantum groups of type \(A_{0|0}\) ⋮ Modified traces for quasi-Hopf algebras ⋮ On Hopf Algebras with Nonzero Integral ⋮ Strongly rational comodules and semiperfect Hopf algebras over QF rings ⋮ On generalized Hopf Galois extensions. ⋮ Morphisms of relative Hopf modules, smash products, and duality ⋮ ABSTRACT ALGEBRAIC INTEGRALS AND FROBENIUS CATEGORIES ⋮ The structure of Hopf algebras with a projection

Cites Work

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• Coreflexive coalgebras
• Reflexivity and coalgebras of finite type
• The uniqueness of integrals for Hopf algebras and some existence theorems of integrals for commutative Hopf algebra
• On the Structure of Ideals of the Dual Algebra of a Coalgebra
• The Order of the Antipode of a Finite Dimensional Hopf Algebra is Finite

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