Download 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 provides a self-contained creation to geometric invariant concept that hyperlinks the elemental thought of affine algebraic teams to Mumford's extra refined concept. The authors systematically make the most the perspective of Hopf algebra concept and the speculation of comodules to simplify and compactify some of the correct formulation and proofs.

The first chapters introduce the topic and assessment the must haves in commutative algebra, algebraic geometry, and the speculation of semisimple Lie algebras over fields of attribute 0. The authors' early presentation of the innovations of activities and quotients is helping to explain the following fabric, relatively within the examine of homogeneous areas. This examine encompasses a exact remedy of the quasi-affine and affine instances and the corresponding strategies of observable and distinctive subgroups.

Among the various 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 routines, which variety from the regimen to the relatively tough, construct services in operating with the basic recommendations. 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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