Technical Actions and Invariants of Algebraic Groups (082475896X)

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Walter Ferrer Santos, Alvaro Rittatore , "Actions and Invariants of Algebraic Groups"

Actions and Invariants of Algebraic Groups presents a self-contained introduction to geometric invariant theory that links the basic theory of affine algebraic groups to Mumford's more sophisticated theory. The authors systematically exploit the viewpoint of Hopf algebra theory and the theory of comodules to simplify and compactify many of the relevant formulas and proofs. The first two chapters introduce the subject and review the prerequisites in commutative algebra, algebraic geometry, and the theory of semisimple Lie algebras over fields of characteristic zero. The authors' early presentation of the concepts of actions and quotients helps to clarify the subsequent material, particularly in the study of homogeneous spaces. This study includes a detailed treatment of the quasi-affine and affine cases and the corresponding concepts of observable and exact subgroups. Among the many other topics discussed are Hilbert's 14th problem, complete with examples and counterexamples, and Mumford's results on quotients by reductive groups. End-of-chapter exercises, which range from the routine to the rather difficult, build expertise in working with the fundamental concepts. The Appendix further enhances this work's completeness and accessibility with an exhaustive glossary of basic definitions, notation, and results.

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	Study The Classical Groups: Their Invariants and Representations The Classical Groups: Their Invariants and RepresentationsPrinceton Univ Pr \| ISBN 0691079234 \| 1946-09 \| PDF \| 336 pages \| 8.61 MBIn this renowned volume, Hermann Weyl discusses the symmetric, full linear, orthogonal, and symplectic group ...
	Science/Engineering Lie Groups: An Approach through Invariants and Representations Procesi C., "Lie Groups: An Approach through Invariants and Representations"Springer; 1 edition (October 12, 2006) \| ISBN-10: 0387260404 \| 608 pages \| PDF \| 25 MbLie groups has been an increasing area of focus and rich research since the m ...
	Encyclopedias Algebraic Geometry IV : Linear Algebraic Groups, Invariant Theory (Encyclopaedia of Mathematical Sciences) Algebraic Geometry IV : Linear Algebraic Groups, Invariant Theory (Encyclopaedia of Mathematical Sciences)Springer \| 1994 \| ISBN: 0387546820 \| Pages: 284 \| DJVU \| 3.30 MBThis volume of the Encyclopaedia contains two contributions on closely ...
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