Actions and Invariants of Algebraic Groups: 2nd Edition (Hardback) book cover

Actions and Invariants of Algebraic Groups

2nd Edition

By Walter Ricardo Ferrer Santos, Alvaro Rittatore

Chapman and Hall/CRC

479 pages | 10 B/W Illus.

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pub: 2016-12-20
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Description

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.

Reviews

"[The new edition of this book] retains all of the attractive features of the first edition and adds new chapters on observable actions (Chapter 15) and geometric invariant theory (Chapter 16)."

- Frank D. Grosshans, Mathematical Reviews, August 2017

Table of Contents

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.

About the Authors

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.

About the Series

Chapman & Hall/CRC Monographs and Research Notes in Mathematics

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Subject Categories

BISAC Subject Codes/Headings:
MAT000000
MATHEMATICS / General
MAT002000
MATHEMATICS / Algebra / General
MAT022000
MATHEMATICS / Number Theory
SCI040000
SCIENCE / Mathematical Physics