Actions and Invariants of Algebraic Groups (2nd Ed.) Chapman & Hall/CRC Monographs and Research Notes in Mathematics Series
Auteurs : Ferrer Santos Walter Ricardo, Rittatore Alvaro
Actions and Invariants of Algebraic Groups, Second Edition presents a self-contained introduction to geometric invariant theory starting from the basic theory of affine algebraic groups and proceeding towards more sophisticated dimensions." Building on the first edition, this book provides an introduction to the theory by equipping the reader with the tools needed to read advanced research in the field. Beginning with commutative algebra, algebraic geometry and the theory of Lie algebras, the book develops the necessary background of affine algebraic groups over an algebraically closed field, and then moves toward the algebraic and geometric aspects of modern invariant theory and quotients.
Algebraic geometry. Lie algebras. Algebraic groups: basic definitions. Algebraic groups: Lie algebras and representations. Algebraic groups: Jordan decomposition and applications. Actions of algebraic groups. Homogeneous spaces. Algebraic groups and Lie algebras in characteristic zero. Observable subgroups of affine algebraic groups. Observable actions of affine algebraic groups. Observable subgroups of affine monoids. Affine homogeneous spaces. Hilbert's 14th problem. Quotients. Appendix. Basic definitions and results.
Walter Ferrer Santos is a professor of mathematics at the University of the Republic, Montevideo, Uruguay.
Alvaro Rittatore is an associate professor of mathematics at the University of the Republic, Montevideo, Uruguay.
Date de parution : 01-2017
17.8x25.4 cm
Thèmes d’Actions and Invariants of Algebraic Groups :
Mots-clés :
Affine Algebraic Group; affine; Algebraic Group; closed; Closed Subgroup; subgroup; Hopf Algebra; lie; Unipotent Groups; algebras; Finitely Generated; finitely; Lie Algebra; generated; Geometric Quotient; variety; Affine Variety; geometric; Algebraic Subgroup; quotient; Geometrically Reductive; Observable Subgroup; Surjective Morphism; Finite Index; Categorical Quotient; Reynolds Operator; Closed Subset; Closed Normal Subgroup; Normal Subgroup; Irreducible Component; Open Subset; Borel Subgroup; Locally Nilpotent; Lie Subalgebra; Jordan Decomposition