Download e-book for iPad: Actions and Invariants of Algebraic Groups (Chapman & by Walter Ferrer Santos,Alvaro Rittatore

By Walter Ferrer Santos,Alvaro Rittatore

activities and Invariants of Algebraic teams provides a self-contained creation to geometric invariant concept that hyperlinks the fundamental concept of affine algebraic teams to Mumford's extra subtle conception. The authors systematically take advantage of 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 assessment 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 techniques of activities and quotients is helping to explain the following fabric, rather within the learn of homogeneous areas. This examine features a designated remedy of the quasi-affine and affine circumstances and the corresponding strategies of observable and specific subgroups.

Among the numerous different issues mentioned are Hilbert's 14th challenge, whole with examples and counterexamples, and Mumford's effects on quotients through reductive teams. End-of-chapter workouts, which variety from the regimen to the really tricky, construct services in operating with the elemental techniques. The Appendix extra complements this work's completeness and accessibility with an exhaustive word list of simple 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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