Best Books on Non commutative algebra.......

[gianeshwar]

Dear friends!
I am interested to study quantum physics at deep level.For that I think I should be well versed with many mathematical tools.Though I have some knowledge of algebra up to Galois Theory and some more related topics of commutative algebra.
I am a mathematics teacher(more a student rather).
From my information I think I need to study non commutative algebra as well.Please tell if I am thinking right or not.Suggest better steps if any. Also suggest some very good books.
I am passionate about beauty of nature and mathematics describing it.

 

[Fredrik]

You will need a solid understanding of complex vector spaces, and linear operators on complex vector spaces. "Linear algebra done wrong" by Sergei Treil will tell you what you need to know about finite-dimensional vector spaces and linear operators on them.

For quantum mechanics, I recommend that you study selected parts of any of the standard introductory texts (I don't know which one is best) and supplement it with "Lectures on quantum theory: Mathematical and structural foundations" by Isham. It's a fairly easy book that focuses on what the theory says, rather than on how to calculate stuff.

If you really want to dig deep into the mathematical aspects of quantum theory, you will need to study topology and functional analysis. Functional analysis is the mathematics of infinite-dimensional vector spaces. You need topology mainly to understand books on functional analysis.

I don't have time to elaborate any further right now, but I might add a few more comments and recommendations later.

 

[micromass]

I'm not sure why you think you need noncommutative algebra. Could you elaborate?
Anyway, a good book on the topic is Lam: https://www.amazon.com/dp/0387953256/?tag=pfamazon01-20

 

[gianeshwar]

Thank you very much friends!
Soon I will reply.