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The Algebra of Invariants
Author: John Hilton Grace
Publisher: American Mathematical Soc.
Published: 1903
Total Pages: 402
ISBN-13:
DOWNLOAD EBOOK →The Theory of Algebraic Number Fields
Author: David Hilbert
Publisher: Springer Science & Business Media
Published: 2013-03-14
Total Pages: 360
ISBN-13: 3662035456
DOWNLOAD EBOOK →A translation of Hilberts "Theorie der algebraischen Zahlkörper" best known as the "Zahlbericht", first published in 1897, in which he provides an elegantly integrated overview of the development of algebraic number theory up to the end of the nineteenth century. The Zahlbericht also provided a firm foundation for further research in the theory, and can be seen as the starting point for all twentieth century investigations into the subject, as well as reciprocity laws and class field theory. This English edition further contains an introduction by F. Lemmermeyer and N. Schappacher.
Representations and Invariants of the Classical Groups
Author: Roe Goodman
Publisher: Cambridge University Press
Published: 2000-01-13
Total Pages: 708
ISBN-13: 9780521663489
DOWNLOAD EBOOK →More than half a century has passed since Weyl's 'The Classical Groups' gave a unified picture of invariant theory. This book presents an updated version of this theory together with many of the important recent developments. As a text for those new to the area, this book provides an introduction to the structure and finite-dimensional representation theory of the complex classical groups that requires only an abstract algebra course as a prerequisite. The more advanced reader will find an introduction to the structure and representations of complex reductive algebraic groups and their compact real forms. This book will also serve as a reference for the main results on tensor and polynomial invariants and the finite-dimensional representation theory of the classical groups. It will appeal to researchers in mathematics, statistics, physics and chemistry whose work involves symmetry groups, representation theory, invariant theory and algebraic group theory.
Theory of Algebraic Invariants
Author: David Hilbert
Publisher: Cambridge University Press
Published: 1993-11-26
Total Pages: 212
ISBN-13: 9780521449038
DOWNLOAD EBOOK →An English translation of the notes from David Hilbert's course in 1897 on Invariant Theory at the University of Gottingen taken by his student Sophus Marxen.
Actions and Invariants of Algebraic Groups
Author: Walter Ricardo Ferrer Santos
Publisher: CRC Press
Published: 2017-09-19
Total Pages: 479
ISBN-13: 1482239167
DOWNLOAD EBOOK →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.
Invariant Theory
Author: T.A. Springer
Publisher: Springer
Published: 2006-11-14
Total Pages: 118
ISBN-13: 3540373705
DOWNLOAD EBOOK →Lectures on Invariant Theory
Author: Igor Dolgachev
Publisher: Cambridge University Press
Published: 2003-08-07
Total Pages: 244
ISBN-13: 9780521525480
DOWNLOAD EBOOK →The primary goal of this 2003 book is to give a brief introduction to the main ideas of algebraic and geometric invariant theory. It assumes only a minimal background in algebraic geometry, algebra and representation theory. Topics covered include the symbolic method for computation of invariants on the space of homogeneous forms, the problem of finite-generatedness of the algebra of invariants, the theory of covariants and constructions of categorical and geometric quotients. Throughout, the emphasis is on concrete examples which originate in classical algebraic geometry. Based on lectures given at University of Michigan, Harvard University and Seoul National University, the book is written in an accessible style and contains many examples and exercises. A novel feature of the book is a discussion of possible linearizations of actions and the variation of quotients under the change of linearization. Also includes the construction of toric varieties as torus quotients of affine spaces.
Algebraic Homogeneous Spaces and Invariant Theory
Author: Frank D. Grosshans
Publisher: Springer
Published: 2006-11-14
Total Pages: 158
ISBN-13: 3540696172
DOWNLOAD EBOOK →The invariant theory of non-reductive groups has its roots in the 19th century but has seen some very interesting developments in the past twenty years. This book is an exposition of several related topics including observable subgroups, induced modules, maximal unipotent subgroups of reductive groups and the method of U-invariants, and the complexity of an action. Much of this material has not appeared previously in book form. The exposition assumes a basic knowledge of algebraic groups and then develops each topic systematically with applications to invariant theory. Exercises are included as well as many examples, some of which are related to geometry and physics.
An Introduction to Invariants and Moduli
Author: Shigeru Mukai
Publisher: Cambridge University Press
Published: 2003-09-08
Total Pages: 528
ISBN-13: 9780521809061
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