Thanks Fallen Angel ... Your post is most helpful ...Fallen Angel said:Hi Peter,
In math exchange you got a thread like this:
reference request - What's a good place to learn Lie groups? - Mathematics Stack Exchange
You can see Fulton-Harris book here:
http://isites.harvard.edu/fs/docs/icb.topic1381051.files/fulton-harris-representation-theory.pdf
and a good-loking course notes here:
http://www.jmilne.org/math/CourseNotes/LAG.pdf
What is your purpose studying Lie theory?
Peter said:Thanks Fallen Angel ... Your post is most helpful ...
My purpose in studying Lie Theory is simply to understand it ... It seems an area that has a wonderful blend of algebra, geometry and analysis ...
My interest was particularly raised recently by an article by Dana Mackenzie in the 2009 booklet "What's Happening in the Mathematical Sciences", about the exceptional Lie Group E8 namely:
"Charting a 248-Dimensional World"
BTW ... Thanks again for your help!
Peter
Thanks Euge,Euge said:Hi Peter,
It looks like you're on the same page as topsquark as far as interests are concerned. This book in the link
Matrix Groups for Undergraduates - Kristopher Tapp - Google Libri
will supply you both with the basics. The Fulton/Harris book is actually intended for a graduate audience (although I've seen the book used for undergraduates) but considering your advanced algebra background, I think you can get through Chapters 1,2,3 and Chapters 7,8,10 with little difficulty.
OK, understand ... Please let let me know about the senior level book when you have had time to form an opinion regarding it ...Euge said:I didn't actually recommend Fulton's book, but my point was, if you decide to work through this book, you'll probably have little difficulty with the chapters I mentioned. I did say that that book is intended for a graduate audience. I have a book on representation theory that's certainly appropriate for senior level students, but I need time to look for it.
Lie theory is a branch of mathematics that studies continuous symmetry and transformation groups, which are essential for understanding the structure and behavior of many physical systems. It is also used in various areas of mathematics such as differential geometry, algebraic geometry, and mathematical physics.
Lie theory has many applications in different fields, such as physics, engineering, and computer science. It is used in the study of differential equations, quantum mechanics, and general relativity. In engineering, it is used in control theory and robotics. In computer science, Lie groups and algebras are used in computer vision and image processing.
A senior undergraduate text on Lie theory and groups is typically aimed at students who have completed their lower division coursework in mathematics and have a strong foundation in linear algebra, calculus, and abstract algebra. It is also suitable for graduate students who want to gain a deeper understanding of the subject.
To study Lie theory and groups, it is recommended to have a background in linear algebra, abstract algebra, and analysis. Familiarity with basic concepts in differential equations and topology can also be helpful. Some knowledge of physics, particularly classical mechanics and electromagnetism, can also aid in understanding the applications of Lie theory.
Yes, there are several online resources available for learning Lie theory and groups. Some recommended resources include lecture notes and videos from universities, online textbooks, and interactive tutorials. Additionally, there are many online forums and communities where students and experts in the field can discuss and share information about Lie theory and groups.