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Actions and Invariants of Algebraic Groupsby Walter Ferrer Santos
CRC Press 2005; US$ 99.95This self-contained introduction to geometric invariant theory links the theory of affine algebraic groups to Mumford's theory. The authors, professors of mathematics at Universidad de la Rep blica, Uruguay, exploit the viewpoint of Hopf algebra theory and the theory of comodules to simplify many of the relevant formulas and proofs. Early chapters more...
Linear Algebraic Monoidsby Lex E. Renner
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG 2005; US$ 149.00The theory of linear algebraic monoids culminates in a coherent blend of algebraic groups, convex geometry, and semigroup theory. The book discusses all the key topics in detail, including classification, orbit structure, representations, universal constructions, and abstract analogues. An explicit cell decomposition is constructed for the wonderful compactification, as is a universal deformation for any semisimple group. A final chapter summarizes important connections with other areas of algebra and geometry. The book will serve as a solid basis for further research. Open problems are discussed as they arise and many useful exercises are included. more...
Classification des Groupes Algébriques Semi-simplesby Pierre Cartier
Springer 2005; US$ 89.95The third volume of the Collected Works of Claude Chevalley assembles his work on semi-simple algebraic groups contained, for the most part, in the notes of the famous "Sminaire Chevalley" held at the Ecole Normale Suprieure in Paris between 1956 and 1958 and written up by participants of the seminar namely, P. Cartier, A. Grothendieck, R. Lazard and J. L. Verdier. These texts have been entirely reset in TeX for this edition, and edited and annotated by Pierre Cartier. Almost 50 years after the original writing, these texts still constitute a choice reference from which to enter and learn this part of the theory of algebraic groups. more...
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