<p>This book presents the characteristic zero invariant theory of finite groups acting linearly on polynomial algebras. The author assumes basic knowledge of groups and rings, and introduces more advanced methods from commutative algebra along the way. The theory is illustrated by numerous examples and applications to physics, engineering, numerical analysis, combinatorics, coding theory, and graph theory. A wide selection of exercises and suggestions for further reading makes the book appropriate for an advanced undergraduate or first-year graduate level course.</p>

Invariant Theory (Student Mathematical Library) (Student Mathematical Library, 36)

Science & Math

Mara D. Neusel

Mathematics

American Mathematical Society

The questions that have been at the center of invariant theory since the 19th century have revolved around the following themes: finiteness, computation, and special classes of invariants. This book begins with a survey of many concrete examples chosen from these themes in the algebraic, homological, and combinatorial context. In further chapters, the authors pick one or the other of these questions as a departure point and present the known answers, open problems, and methods and tools needed to obtain these answers. Chapter 2 deals with algebraic finiteness. Chapter 3 deals with combinatorial finiteness. Chapter 4 presents Noetherian finiteness. Chapter 5 addresses homological finiteness. Chapter 6 presents special classes of invariants, which deal with modular invariant theory and its particular problems and features. Chapter 7 collects results for special classes of invariants and coinvariants such as (pseudo) reflection groups and representations of low degree. If the ground field is finite, additional problems appear and are compensated for in part by the emergence of new tools. One of these is the Steenrod algebra, which the authors introduce in Chapter 8 to solve the inverse invariant theory problem, around which the authors have organized the last three chapters. The book contains numerous examples to illustrate the theory, often of more than passing interest, and an appendix on commutative graded algebra, which provides some of the required basic background. There is an extensive reference list to provide the reader with orientation to the vast literature.

Invariant Theory of Finite Groups (Mathematical Surveys and Monographs) (Mathematical Surveys and Monographs, 94)

Larry Smith

See the best price to sell, buy, or rent books by Mara D. Neusel. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

Books by Mara D. Neusel

See the best price to sell, buy, or rent books by Mara D. Neusel. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

Invariant Theory (Student Mathematical Library) (Student Mathematical Library, 36)

Invariant Theory of Finite Groups (Mathematical Surveys and Monographs) (Mathematical Surveys and Monographs, 94)