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

By Walter Ferrer Santos,Alvaro Rittatore

activities and Invariants of Algebraic teams offers a self-contained advent to geometric invariant idea that hyperlinks the elemental thought of affine algebraic teams to Mumford's extra refined conception. The authors systematically make the most the point of view of Hopf algebra conception and the idea of comodules to simplify and compactify a few of the suitable 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 strategies of activities and quotients is helping to elucidate the next fabric, quite within the examine of homogeneous areas. This examine encompasses a designated remedy of the quasi-affine and affine situations and the corresponding recommendations of observable and special subgroups.

Among the numerous different themes mentioned are Hilbert's 14th challenge, whole with examples and counterexamples, and Mumford's effects on quotients by means of reductive teams. End-of-chapter workouts, which diversity from the regimen to the particularly tricky, construct services in operating with the elemental recommendations. The Appendix additional 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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