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**Elements of mathematics. Lie groups and Lie algebras. Chapters 4–6. Transl. from the French by Andrew Pressley.**
*(English)*
Zbl 0983.17001

Berlin: Springer. xi, 300 p. (2002).

This book is an English translation of the classical volume initially published in French (1968; Zbl 0186.33001) and reviewed by E. Abe. A translation into Russian has also been published. Contents: Chapter 4: Coxeter groups and Tits systems. Chapter 5: Groups generated by reflections. Chapter 6: Root systems.

For Chapters 1-3 (Springer 1998) see Zbl 0904.17001.

For Chapters 1-3 (Springer 1998) see Zbl 0904.17001.

Reviewer: A.Akutowicz (Berlin)

### MSC:

17-02 | Research exposition (monographs, survey articles) pertaining to nonassociative rings and algebras |

22-02 | Research exposition (monographs, survey articles) pertaining to topological groups |

22E10 | General properties and structure of complex Lie groups |

22E15 | General properties and structure of real Lie groups |

22E60 | Lie algebras of Lie groups |

17B20 | Simple, semisimple, reductive (super)algebras |

20E42 | Groups with a \(BN\)-pair; buildings |

20F55 | Reflection and Coxeter groups (group-theoretic aspects) |

51F15 | Reflection groups, reflection geometries |

### Keywords:

semisimple Lie algebras; Weyl groups; root systems; Coxeter groups; Tits systems; reflection groups
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\textit{N. Bourbaki}, Elements of mathematics. Lie groups and Lie algebras. Chapters 4--6. Transl. from the French by Andrew Pressley. Berlin: Springer (2002; Zbl 0983.17001)

### Online Encyclopedia of Integer Sequences:

Dimensions of the irreducible representations of the simple Lie algebra of type G2 over the complex numbers, listed in increasing order.Dimensions of the irreducible representations of the algebraic group SL4 (equivalently, simple Lie algebra of type A3) over the complex numbers, listed in increasing order.

Dimensions of the irreducible representations of the simple Lie algebra of type E7 over the complex numbers, listed in increasing order.

Dimensions of the irreducible representations of the simple Lie algebra of type E6 over the complex numbers, listed in increasing order.

Dimensions of the irreducible representations of the simple Lie algebra of type F4 over the complex numbers, listed in increasing order.

Dimensions of the irreducible representations of the simple Lie algebra of type D4 over the complex numbers, listed in increasing order.

Dimensions of the irreducible representations of the simple Lie algebra of type A2 (equivalently, the group SL3) over the complex numbers, listed in increasing order.

List of dimensions for which there exist several non-isomorphic irreducible representations of E6.

List of dimensions for which there exist several non-isomorphic irreducible representations of E7.

List of dimensions for which there exist 8 or more non-isomorphic irreducible representations of E6.