Bourbaki, Nicolas 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. Reviewer: A.Akutowicz (Berlin) Cited in 6 ReviewsCited in 260 Documents 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 Citations:Zbl 0186.33001; Zbl 0249.22001; Zbl 0483.22001; Zbl 0904.17001 PDF BibTeX XML Cite \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) OpenURL 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.