Hopf algebras : an introduction

Detalles Bibliográficos
Autor principal: Dăscălescu, Sorin
Otros Autores: Năstăsescu, C. (Constantin), 1943-, Raianu, Șerban
Formato: Libro
Lenguaje:English
Publicado: New York : Marcel Dekker, ©2001.
Colección:Monographs and textbooks in pure and applied mathematics ; 235.
Materias:
Álgebra de Hopf
Acceso en línea:http://catdir.loc.gov/catdir/enhancements/fy0647/00059025-d.html
Tabla de Contenidos:
  • 1. Algebras and coalgebras
  • 1.1. Basic concepts
  • 1.2. The finite topology
  • 1.3. The dual (co)algebra
  • 1.4. Constructions in the category of coalgebras
  • 1.5. The finite dual of an algebra
  • 1.6. The cofree coalgebra
  • 2. Comodules
  • 1.1. The category of comodules over a coalgebra
  • 2.2. Rational modules
  • 2.3. Bicomodules and the cotensor product
  • 2.4. Simple comodules and injective comodules
  • 2.5. Some topics on torsion theories on M[superscript C]
  • 3. Special classes of coalgebras
  • 3.1. Cosemisimple coalgebras
  • 3.2. Semiperfect coalgebras
  • 3.3. (Quasi)co-Frobenius and co-Frobenius coalgebras
  • 4. Bialgebras and Hopf algebras
  • 4.1. Bialgebras
  • 4.2. Hopf algebras
  • 4.3. Examples of Hopf algebras
  • 4.4. Hopf modules
  • 5. Integrals
  • 5.1. The definition of integrals for a bialgebra
  • 5.2. The connection between integrals and the ideal H[superscript *rat]
  • 5.3. Finiteness conditions of Hopf algebras with nonzero integrals
  • 5.4. The uniqueness of integrals and the bijectivity of the antipode
  • 5.5. Ideals in Hopf algebras with nonzero integrals
  • 5.6. Hopf algebras constructed by Ore extensions
  • 6. Actions and coactions of Hopf algebras
  • 6.1. Actions of Hopf algebras on algebras
  • 6.2. Coactions of Hopf algebras on algebras
  • 6.3. The Morita context
  • 6.4. Hopf-Galois extensions
  • 6.5. Application to the duality theorems for co-Frobenius Hopf algebras
  • 7. Finite dimensional Hopf algebras
  • 7.1. The order of the antipode
  • 7.2. The Nichols-Zoeller Theorem
  • 7.3. Matrix subcoalgebras of Hopf algebras
  • 7.4. Cosemisimplicity, semisimplicity, and the square of the antipode
  • 7.5. Character theory for semisimple Hopf algebras
  • 7.6. The Class Equation and applications
  • 7.7. The Taft-Wilson Theorem
  • 7.8. Pointed Hopf algebras of dimension p[superscript n] with large coradical
  • 7.9. Pointed Hopf algebras of dimension p[superscript 3]
  • A. The category theory language
  • B. C-groups and C-cogroups.

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