Actions and Invariants of Algebraic Groups (Chapman & by Walter Ferrer Santos,Alvaro Rittatore PDF

By Walter Ferrer Santos,Alvaro Rittatore

activities and Invariants of Algebraic teams offers a self-contained advent to geometric invariant thought that hyperlinks the elemental conception of affine algebraic teams to Mumford's extra subtle thought. The authors systematically make the most the perspective of Hopf algebra concept and the idea of comodules to simplify and compactify a number of the proper formulation and proofs.

The first chapters introduce the topic and evaluation the necessities in commutative algebra, algebraic geometry, and the idea of semisimple Lie algebras over fields of attribute 0. The authors' early presentation of the options of activities and quotients is helping to elucidate the following fabric, really within the learn of homogeneous areas. This examine encompasses a unique remedy of the quasi-affine and affine circumstances and the corresponding ideas of observable and precise subgroups.

Among the numerous different issues 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 variety from the regimen to the fairly tricky, construct services in operating with the basic options. The Appendix extra complements this work's completeness and accessibility with an exhaustive word list 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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