Read e-book online Actions and Invariants of Algebraic Groups (Chapman & PDF

By Walter Ferrer Santos,Alvaro Rittatore

activities and Invariants of Algebraic teams provides a self-contained advent to geometric invariant idea that hyperlinks the fundamental idea of affine algebraic teams to Mumford's extra subtle conception. The authors systematically make the most the point of view of Hopf algebra concept and the idea of comodules to simplify and compactify a few of the suitable formulation and proofs.

The first chapters introduce the topic and overview the necessities in commutative algebra, algebraic geometry, and the speculation of semisimple Lie algebras over fields of attribute 0. The authors' early presentation of the thoughts of activities and quotients is helping to elucidate the following fabric, quite within the learn of homogeneous areas. This learn contains a specific remedy of the quasi-affine and affine instances and the corresponding recommendations of observable and specified subgroups.

Among the various different themes mentioned are Hilbert's 14th challenge, whole with examples and counterexamples, and Mumford's effects on quotients through reductive teams. End-of-chapter routines, which variety from the regimen to the particularly tricky, construct services in operating with the basic innovations. The Appendix additional complements this work's completeness and accessibility with an exhaustive thesaurus of easy 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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