» » Invariant Theory (Student Mathematical Library)

Download Invariant Theory (Student Mathematical Library) epub

by Mara D. Neusel

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.
Download Invariant Theory (Student Mathematical Library) epub
ISBN: 0821841327
ISBN13: 978-0821841327
Category: Science
Subcategory: Mathematics
Author: Mara D. Neusel
Language: English
Publisher: American Mathematical Society (December 19, 2006)
Pages: 314 pages
ePUB size: 1403 kb
FB2 size: 1181 kb
Rating: 4.5
Votes: 976
Other Formats: mbr doc lrf azw

This text is a useful compilation of results in invariant theory, but it is unfortunately full of mistakes, both small and large: errors of fact, oversimplifications, theorems that are true but proven incorrectly, ambiguities, etc. You'll want to check every assertion.
Along with new material this text is an improvement.
I'm physically disappointed that important groups like U(1)*su(2),Cartan A_2, A_4
and D_5 aren't covered, but D_10 is included.
I'm a goal oriented physics type who uses computer algebra
system to generate Molien sequences and am interested in their implications
as linear transfer functions in graph based systems theory.
For many years the standard text has been:
Polynomial Invariants of Finite Groups (London Mathematical Society Lecture Note Series)
This current book although better is still not
one you could give to undergrads in chemistry and physics.
This is the smartest book and reader-friendliest - if not the only textbook - on Invariant Theory ever written for undergraduates. Clearly, the previous review was written by an undergraduate.... at heart. I am one of the people who reviewed the book in part and yes, there might be a few small errors here and there (all the books have a few.... and yes, people who write very few books and papers NEVER make mistakes), but there are no serious mistakes / no mistakes that could not be easily figured out or fixed. I would even challenge my better students to find these errors - for credit!! The book offers not only an exquisite introduction to Invariant Theory, but a never-before-tried relationship to other fields, such as physics, algebra, group theory, even differential geometry. Happy reading!
-- some books need more than one editor --

where to begin?
the subject matter before us, namely the invariant
theory of finite groups, comprises a beautiful chapter
in mathematics -- unfortunately, you'd never guess it
from this book --
the approach is relentlessly algebraic with little or no
guidance as to why one is investing such effort in page
after page of calculation --
aside from the fact that the author does not exactly possess a
gift for exposition, there are several unforgivable lapses:

a) when there are too many errors, it erodes the trust of the
reader who is forced to essentially proofread every line
[the author did not keep her promise to provide an errata
list --- the list that does appear refers to another title]

b) it is criminal not to mention in an introductory work the
obvious geometric significance of some of the lower degree
invariants -- one is essentially working blind

c) the so called "applications" are a joke and even more forced
than the ones that pop up in undergrad calc books -- take the
example of 'application to weighted graphs' which occupies all
of one page -- by the time she defines what graphs are there is
no space left for examples or illustrations -- the result is
embarrassing rather than edifying

d) the bibliography is stingy in the extreme -- it is particularly
galling that Sloane's 1977 paper was not cited -- anyone interested
in this subject would do infinitely better to read this short (~30 pgs)
paper to get a great feel not only for pertinent examples but also a
good historical overview and even some classy tie-ins with other branches
of math
in short: a decent introductory text in this area has yet to be writ