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¡¶²©Ê¿ºóÎÄ¿â¡·ÐòÑÔ Preface Chapter 1 The Green Rings of Hopf Algebras 1.1 Hopf algebras 1.2 Quantum traces ofmorphisms 1.3 Bilinear forms on Green rings 1.4 Some ring¡ªtheoretical properties Chapter 2 The Green Rings of Spherical Hopf Algebras 2.1 A new bilinear form 2.2 Quotients of Green rings 2.3 Group¡ªlike algebra and bi¡ªFrobenius algebra structure Chapter 3 The Stable Green Rings of Hopf Algebras 3.1 Stable Green rings 3.2 Bi¡ªFrobenius algebra structure 3.3 Applications to Radford Hopf algebras Chapter 4 The Caslmlr Numbers of Green Rings 4.1 The Jacobson semisimplicity of Green rings 4.2 The Green ring of a cyclic group 4.3 The Casimir number of the Green ring of a cyclic group Chapter 5 The Casimir Numbers of Fusion Categories 5.1 Numerical invariants 5.2 Applications to Verlinde modular categories 5.3 Prime factors of Casimir numbers 5.4 Casimir numbers VS.Frobenius¡ªSchur exponents Chapter 6 Higher Frobenius.Schur Indicators in Positive Characteristic 6.1 Characterizations of S2=id 6.2 Some properties of the element U 6.3 Higher Frobenius¡ªSchur indicators 6.4 Monoidal invariantS Chapter 7 The Grothendieck Algebras of Smash Product Hopf Algebras 7.1 Smash product Hopf algebras 7.2 Representations of smash product Hopf algebras 7.3 The Grothendieck algebras of smash product Hopf algebras Chapter 8 Invariants from the Sweedler Power Maps on Integrals 8.1 The Sweedler power maps on integrals 8.2 Polynomial invariants 8.3 Examples 8.4 Integrals of the dual of twisted Hopf algebras Bibliography Index ±àºó¼Ç