Collected works 3

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The third volume of the Collected Works of Claude Chevalley compiles his contributions to semi-simple algebraic groups, primarily derived from the renowned "Séminaire Chevalley" held at the École Normale Supérieure in Paris from 1956 to 1958. The seminar notes, written by participants including P. Cartier, A. Grothendieck, R. Lazard, and J. L. Verdier, have been meticulously reset in TeX for this edition and edited by Pierre Cartier. Nearly five decades later, these texts remain a vital resource for those looking to delve into the theory of algebraic groups. The volume includes sections on the definition of algebraic varieties, schemes, algebraic groups, commutative affine algebraic groups, and fundamental structure theorems for affine algebraic groups. It also covers topics such as Cartan subgroups, regular elements, homogeneous spaces, normalizers of Borel groups, singular tori, the Weyl group, roots, and the structure of semi-simple groups. Additional discussions on finite groups generated by reflections, linear systems on G/B, dominant weights, radical subgroups, isogenies, Dynkin diagrams, and groups of types An, G2, and Cn are included. The volume concludes with an index, making it a comprehensive reference for scholars in the field.