Extension theory for connected Hopf algebras

DOI10.1016/0021-8693(72)90031-2zbMath0269.16011OpenAlexW1988404160MaRDI QIDQ2563192

William M. Singer

Publication date: 1972

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

Full work available at URL: https://doi.org/10.1016/0021-8693(72)90031-2

Mathematics Subject Classification ID

Centralizing and normalizing extensions (16S20)

Related Items

Extensions of locally compact quantum groups and the bicrossed product construction. ⋮ Cohomology of unipotent algebraic and finite groups and the Steenrod algebra ⋮ Bicrossproduct Hopf superalgebras and D=4 κ-deformed Poincaré supergroup ⋮ On the notion of exact sequence: From Hopf algebras to tensor categories ⋮ Unnamed Item ⋮ Cohomology of Abelian matched pairs and the Kac sequence. ⋮ Bicrossproduct structure of \(\kappa\)-Poincaré group and non-commutative geometry. ⋮ Low dimensional cocommutative connected Hopf algebras ⋮ Calculations of some groups of Hopf algebra extensions ⋮ Semisimple Hopf algebras of dimension \(6\), \(8\) ⋮ Spectral sequences for the classification of extensions of Hopf algebras ⋮ Hopf algebra extensions of monogenic Hopf algebras ⋮ Weak crossed biproducts and weak projections. ⋮ Bicrossproduct vs. twist quantum symmetries in noncommutative geometries: the case of \(\varrho\)-Minkowski ⋮ Bicocycle double cross constructions ⋮ Discrete dynamical systems over double cross-product Lie groupoids ⋮ Connected Hopf algebras of dimension \(p^2\). ⋮ The Serre spectral sequence of a multiplicative fibration ⋮ EXAMPLES OF POINTED COLOR HOPF ALGEBRAS ⋮ Classification of semisimple Hopf algebras of dimension 16 ⋮ CLASSIFYING COALGEBRA SPLIT EXTENSIONS OF HOPF ALGEBRAS ⋮ Steenrod Squares in Spectral Sequences. II ⋮ Cross product bialgebras. II ⋮ Principal bundles and group extensions with applications to Hopf algebras ⋮ More examples of bicrossproduct and double cross product Hopf algebras ⋮ Classification of connected Hopf algebras of dimension \(p^3\). I. ⋮ Hopf algebra orders determined by group valuations ⋮ Matched pairs of groups and bismash products of hopf algebras ⋮ Construction of higher groupoids via matched pairs actions ⋮ A five-term exact sequence for Kac cohomology ⋮ Hopf algebras arising from partial (co)actions ⋮ Extensions of Hopf Algebras and Lie Bialgebras ⋮ Hopf bimodules, coquasibialgebras, and an exact sequence of Kac ⋮ Cohomologies and extensions in monoidal categories ⋮ Some properties of cohomologies in monoidal categories ⋮ Cohomology and coquasi-bialgebra extensions associated to a matched pair of bialgebras ⋮ Isomorphism classes of finite dimensional connected Hopf algebras in positive characteristic.

Cites Work

• Unnamed Item
• Unnamed Item
• On the structure of Hopf algebras
• On the groups \(H(\Pi,n)\). I
• On Extensions of Algebras, Co-Algebras and Hopf Algebras, I
• Cocommutative Hopf algebras with antipode