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 creation to geometric invariant conception that hyperlinks the fundamental 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 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 ideas of activities and quotients is helping to explain the following fabric, rather within the learn of homogeneous areas. This examine encompasses a precise therapy of the quasi-affine and affine instances and the corresponding recommendations of observable and distinctive subgroups.

Among the numerous different themes mentioned are Hilbert's 14th challenge, whole with examples and counterexamples, and Mumford's effects on quotients via reductive teams. End-of-chapter workouts, which diversity 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 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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