دانلود کتاب Hopf algebras

فهرست مطالب :

Basic notions from category theory
Categories and functors
Categories
Functors
Natural transformations
Adjoint functors
Equivalences and isomorphisms of categories
Abelian categories
Equalizers and coequalizers
Kernels and cokernels
Limits and colimits
Abelian categories and Grothendieck categories
Exact functors
Grothendieck categories
Tensor products of modules
Universal property
Existence of tensor product
Iterated tensor products
Tensor products over fields
Tensor products over arbitrary algebras
Monoidal categories and algebras
Monoidal categories and coherence
Monoidal functors
Symmetric and braided monoidal categories
Hopf algebras
Monoidal categories and bialgebras
Hopf algebras and duality
The convolution product, the antipode and Hopf algebras
Projective modules
Duality
Properties of coalgebras
Examples of coalgebras
Subcoalgebras and coideals
Comodules
Examples of Hopf algebras
Hopf modules and integral theory
Integrals and separability
Hopf modules and the fundamental theorem
Galois Theory
Algebras and coalgebras in monoidal categories
Corings
Faithfully flat descent
Galois corings
Morita Theory
Galois corings and Morita theory
Hopf-Galois extensions
Strongly graded rings
Classical Galois theory
Examples from (non-commutative) geometry
The general philosophy
Hopf algebras in algebraic geometry
Coordinates as monoidal functor
A glimpse on non-commutative geometry
Non-commutative geometry by Hopf (Galois) theory
Deformations of algebraic groups: algebraic quantum groups
More quantum groups