霍普夫代數

Preface

Notation

1 Modules and algebras

1．Modules

2．Algebras over a commutative ring

3．Lie algebras

4．Semi-simple algebras

5．Finitely generated commutative algebras

2 Hopf algebras

1．Bialgcbras and Hopf algebras

2．The representative bialgebras of semigroups

3．The duality between algebras and coalgebras

4．Irreducible bialgebras　

5．Irreducible cocommutative biaIgebras

3 Hopr algebras and relnmmamtlom of group

1．Comodules and bimodules

2．Bimodules and biaIgebms

3．Integrals for Hopf algebras

4．The duality theorem　

4 ApplimlJons to algebraic groups　

1．Affme k-varieties　

2．Atone k-groups

3．Lie algebras of affme algebraic k-groups

4．Factor groups

5．Unipotent groups and solvable groups

6．Completely reducible groups

5 Applications to field theory

1．K／k—bialgebras

2．Jacobson's theorem

3．Modular extensions

Appendix：Categories and functors

A．1 Categories

A．2 Functors

A．3 Adjoint functors

A．4 Representable functors

A．5 φ-groups andφ-cogroups

References

Index