## Advances in Hopf Algebras"This remarkable reference covers topics such as quantum groups, Hopf Galois theory, actions and coactions of Hopf algebras, smash and crossed products, and the structure of cosemisimple Hopf algebras. " |

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### Contents

Quantum Commutativity and Central Invariants | 25 |

Generalized Smash Products and Morita Contexts for Arbitrary | 39 |

Algebras and Hopf Algebras in Braided Categories | 55 |

Quotient Theory of Hopf Algebras | 107 |

Cosemisimple Hopf Algebras | 135 |

Endomorphism Bialgebras of Diagrams and of Noncommutative Algebras | 153 |

The Almost Right Connes Spectrum | 187 |

On Kauffmans Knot Invariants Arising from FiniteDimensional | 205 |

Hopf Galois Extensions Crossed Products and Clifford Theory | 267 |

Algebraic Aspects of Linearly Recursive Sequences | 299 |

Relations of Representations of Quantum Groups and Finite Groups | 319 |

### Common terms and phrases

A-module action of H adjoint algebra H algebra homomorphism algebra map algebra structure antipode assume bialgebra bijective braided category braided groups coaction coalgebra cocommutative coend(w commutative comodule algebras comultiplication construction COROLLARY crossed product defined denote divided-power dual quasitriangular endomorphism equation example factorizable faithfully flat finite finite-dimensional Hopf algebra following are equivalent formal group functor Galois extension given group algebra H-comodule Hence Hopf Galois extensions Hopf modules Hopf subalgebra ideal induced invariants irreducible isomorphism knot left integral left module Lemma Let H Lie algebra linearly recursive sequences Majid Math matrix module structure monoidal category morphisms multiplication non-commutative non-zero object polynomial Proof Proposition quantum groups quantum spaces quasitriangular Hopf algebra quasitriangular structure quotient recursive relation representation resp result ribbon element ribbon Hopf algebra right coideal subalgebra right integral ring root of unity satisfies smash product Suppose surjective tensor product Theorem theory vector spaces