霍普夫代數（簡體書）

《霍普夫代數(英文版)》內容為：If for instance, we replace the finite group G in the above argumentby a topological group and k by the field of real numbers or the field ofcomplex numbers, or if we take G to be an algebraic group over analgebraically closed field k and A is replaced by the k-algebra of allcontinuous representative functions or of all regular functions over G,then A turns out to be a k-Hopf algebra in exactly the same manner.These algebraic systems play an important role when studying thestructure of G. Similarly, a k-Hopf algebra structure can be definednaturally on the universal enveloping algebra of a k-Lie algebra.The universal enveloping algebra of the Lie algebra of asemi-simple algebraic group turns out to be （in a sense） the dual oftheHopf algebra defined above. These constitute some of the mostnatural examples of Hopf algebras. The general structure of suchalgebraic systems hasHofp代數概念首次是被引進到代數拓撲理論，而近些年將其發展並應用於數學的其他領域，比如李群，代數群以及Galois理論。本書修訂並譯自日語，是學習Hopf代數基本理論的入門書籍。在介紹和討論了上代數、雙代數以及Hofp代數以後，接著講述Hopf代數積分的獨特性和存在性的Sullivan證明以及雙模基本結構理論。Hopf代數和群之間的對偶性引入仿射K-群的定義，通過Hopf代數理論的應用討論了因子群的結構，可分解群的結構和完全可約群。最後，簡單介紹了不可分域的Galois理論。目次：模型與代數；Hopf代數；Hopf代數與群表示論；代數群中的應用；域論中的應用。
讀者對象：本書適用於代數領域的研究生以及科研人員。

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．Jacobsons 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