# Algebras, Rings and Modules: Lie Algebras and Hopf Algebras

### About this Title

**Michiel Hazewinkel**, **Nadiya Gubareni**, *Technical University of Czȩstochowa, Czȩstochowa, Poland* and **V. V. Kirichenko**, *Kiev National Taras Shevchenko University, Kiev, Ukraine*

Publication: Mathematical Surveys and Monographs

Publication Year:
2010; Volume 168

ISBNs: 978-0-8218-5262-0 (print); 978-1-4704-1395-8 (online)

DOI: https://doi.org/http://dx.doi.org/10.1090/surv/168

MathSciNet review: MR2724822

MSC: Primary 16T05; Secondary 16-02, 17-02

### Table of Contents

**Front/Back Matter**

**Chapters**

- 1. Lie algebras and Dynkin diagrams
- 2. Coalgebras: Motivation, definitions, and examples
- 3. Bialgebras and Hopf algebras. Motivation, definitions, and examples
- 4. The Hopf algebra of symmetric functions
- 5. The representations of the symmetric groups from the Hopf algebra point of view
- 6. The Hopf algebra of noncommutative symmetric functions and the Hopf algebra of quasisymmetric functions
- 7. The Hopf algebra of permutations
- 8. Hopf algebras: Applications in and interrelations with other parts of mathematics and physics