In summary, Richard Pierce's book [2] aims to demonstrate that there is more to algebra than just Galois theory. He explains that although Galois theory may not be of interest to physicists, many other types of algebras are, such as tensor algebras, Banach algebras, Lie and Virasoro algebras, and supermanifolds. This article serves as a guide to the diverse world of algebras, introducing readers to famous mathematicians and physicists along the way.
  • #1
fresh_42
Mentor
Insights Author
2023 Award
18,994
23,950

Introduction to the World of Algebras​


Richard Pierce describes the intention of his book [2] about associative algebras as his attempt to prove that there is algebra after Galois theory. Whereas Galois theory might not really be on the agenda of physicists, many algebras are: from tensor algebras as the gown for infinitesimal coordinates over Graßmann and Banach algebras for the theory of differential forms and functions up to Lie and Virasoro algebras in quantum physics and supermanifolds. This article is meant to provide a guide and a presentation of the main parts of this zoo of algebras. And we will meet many famous mathematicians and physicists on the way.

Continue reading...
 
Last edited:
  • Like
  • Informative
Likes bhobba, pinball1970, DeBangis21 and 6 others

Similar threads

  • Science and Math Textbooks
Replies
9
Views
3K
  • Science and Math Textbooks
Replies
7
Views
3K
  • Science and Math Textbooks
Replies
5
Views
6K
Replies
17
Views
4K
  • MATLAB, Maple, Mathematica, LaTeX
Replies
4
Views
9K
  • MATLAB, Maple, Mathematica, LaTeX
Replies
2
Views
2K
  • Linear and Abstract Algebra
Replies
3
Views
10K
  • MATLAB, Maple, Mathematica, LaTeX
2
Replies
39
Views
4K
  • MATLAB, Maple, Mathematica, LaTeX
Replies
4
Views
2K
Replies
4
Views
1K
Back
Top