Books on Character theory and category theory

In summary, the conversation is about the request for book recommendations on character theory and category theory, with a preference for mathematically rigorous books. The mention of Isaacs and Mac Lane as authors for characters and categories, respectively, is noted. There is also a question about the prevalence of books on finite groups when searching for character theory.
  • #1
mrandersdk
246
1
As the title says i would like to get recommended some books on Character theory and category theory. I like my books to be really matematically and to not skip corners, but I don't like books that think that I'm a master mind and just write 'clear' or 'easy' instead of proving the theorem.

Anyone got some ideas ?
 
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  • #2
Characters (of finite groups): Isaacs. (The term characters is very ambiguous.)
Categories: Mac Lane.
 
  • #3
Are there any reason that most books are on finite groups when i make a search on it?

I don't know much about characters, only seen them in my course on lie groups, but i guess they aren't on finite groups.
 

1. What is character theory and category theory?

Character theory and category theory are two distinct branches of mathematics. Character theory deals with the representation theory of finite groups, while category theory is a branch of abstract algebra that studies mathematical structures and their relationships.

2. How are character theory and category theory related?

Character theory and category theory are related through their use of abstract algebraic concepts and their focus on understanding mathematical structures and their properties.

3. What are the key concepts in character theory?

The key concepts in character theory include group representations, character tables, and the character ring. These concepts are used to study the structure and behavior of finite groups.

4. What are the key concepts in category theory?

The key concepts in category theory include categories, functors, and natural transformations. These concepts are used to study the relationships between mathematical structures and the properties that they share.

5. How are character theory and category theory applied in other fields?

Character theory and category theory have applications in various fields, including algebraic geometry, topology, and theoretical physics. They provide powerful tools for understanding and analyzing complex mathematical structures and systems.

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