Lie Algebras and Algebraic Groups (Springer Monographs in Mathematics)

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Oxford Grad. Texts in Math. Stembridge, J.

1.1 What is a Lie Algebra?

Graduate Studies in Math. Neusel, M. Surveys and Monographs vol 94, AMS, Lakshmibai, Peter Littleman, C. Seshadri, Schubert Varieties. Kane, Reflection groups and invariant theory. CMS Books in Math. July August Rossmann, Lie Groups -- An introduction through linear groups. Kumar, Kac-Moody groups, their flag varieties and representation theory.

Nihon-Hyoron-sha, July Bruce E. Sagan, The symmetric group 2nd ed.

Lie Groups and their lattices

Library 56, North-Holland, Bertram, The geometry of Jordan and Lie structures. LNM , Springer, Geck and G. Mmonographs 21, Oxford, Japan, Dunkl and Y. Xu, Orthogonal polynomials of several variables, Encyclopedia of Math. Press, Society, Heyer, T. Hirai and N. Obata eds. Frappat, A. It seems that you're in Germany. We have a dedicated site for Germany. Authors: Onishchik , Arkadij L. Our guiding idea was to present in the most economic way the theory of semisimple Lie groups on the basis of the theory of algebraic groups.

Our main sources were A.

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Borel's paper [34], C. ChevalIey's seminar [14], seminar "Sophus Lie" [15] and monographs by C. Chevalley [4], N. Jacobson [9] and J-P. Results on topological spaces 1. Rings and modules 2.

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Integral extensions 3. Factorial rings 4.

Normalizers and self-normalizing subgroups

Field extensions 5. Finitely generated algebras 6.

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Gradings and filtrations 7. Inductive limits 8. Sheaves of functions 9. Jordan decomposition and some basic results on groups Algebraic sets Prevarieties and varieties Projective varieties Dimension Morphisms show more. Review Text From the reviews: "As Tauvel and Yu focus on algebraic groups, they approach Lie theory via algebraic geometry and even develop that subject from scratch For the purpose at hand, Tauvel and Yu's work compares favorably Summing Up: Highly recommended.

Upper-division undergraduates through professionals. Feldman, Choice, , June "The sheer volume of material covered herein should make this book an invaluable reference for people interested in, or teaching, Lie algebras or algebraic groups. It truly provides 'one stop shopping' for someone needing a result or hard-to-find proof.

I cannot even begin to imagine how much work must have gone into creating such a thorough and comprehensive reference, and I have no doubt it will be an important and useful addition to the literature on this subject. Therefore this book is an ideal reference source and research guide for graduate students and mathematicians working in this area. The aim of this book is to assemble in a single volume the algebraic aspects of the theory, so as to present the foundations of the theory in characteristic zero.

Detailed proofs are included and some recent results are discussed in the final chapters. The book has an encyclopedic character, offering much else besides the actual subject. Complete proofs are given and the authors present their material clearly and concisely throughout.