Get Actions and Invariants of Algebraic Groups (Chapman & PDF

By Walter Ferrer Santos,Alvaro Rittatore

activities and Invariants of Algebraic teams offers a self-contained creation to geometric invariant conception that hyperlinks the elemental concept of affine algebraic teams to Mumford's extra refined idea. The authors systematically take advantage of the point of view of Hopf algebra thought and the idea of comodules to simplify and compactify some of the correct 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 recommendations of activities and quotients is helping to elucidate the next fabric, relatively within the learn of homogeneous areas. This examine contains a designated remedy of the quasi-affine and affine instances and the corresponding options of observable and designated subgroups.

Among the numerous different subject matters mentioned are Hilbert's 14th challenge, entire with examples and counterexamples, and Mumford's effects on quotients by means of reductive teams. End-of-chapter workouts, which variety from the regimen to the quite tough, construct services in operating with the basic strategies. 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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