Actions and Invariants of Algebraic Groups (Chapman & by Walter Ferrer Santos,Alvaro Rittatore PDF

By Walter Ferrer Santos,Alvaro Rittatore

activities and Invariants of Algebraic teams provides a self-contained advent to geometric invariant thought that hyperlinks the fundamental thought of affine algebraic teams to Mumford's extra subtle conception. The authors systematically take advantage of the point of view of Hopf algebra thought and the speculation of comodules to simplify and compactify the various appropriate formulation and proofs.

The first chapters introduce the topic and evaluate the must haves in commutative algebra, algebraic geometry, and the idea of semisimple Lie algebras over fields of attribute 0. The authors' early presentation of the suggestions of activities and quotients is helping to explain the next fabric, relatively within the examine of homogeneous areas. This examine incorporates a distinct remedy of the quasi-affine and affine instances and the corresponding thoughts of observable and distinct subgroups.

Among the numerous different issues mentioned are Hilbert's 14th challenge, entire with examples and counterexamples, and Mumford's effects on quotients by way of reductive teams. End-of-chapter routines, which diversity from the regimen to the relatively tough, construct services in operating with the elemental innovations. The Appendix additional complements this work's completeness and accessibility with an exhaustive thesaurus of uncomplicated definitions, notation, and results.

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Actions and Invariants of Algebraic Groups (Chapman & Hall/CRC Monographs and Research Notes in Mathematics) by Walter Ferrer Santos,Alvaro Rittatore

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