10:00 - 4:30
Today, I studied the core of basic Lie algebra representation theory. Representation theory, as stated before, revolve around "homomorphisms," a kind of functions, from a Lie algebra to the set of self-transformations of a vector space. One of the most important theorems that my mentor described to me was Schur's Lemma, which requires too much background information to be described in a single blog post. However, even though it is considered to be very "elementary," it has a lot of applications in proving stronger and much more complicated theorems. Lastly, towards the end of the internship, my mentor referred again to the very general "category theory," and how even Lie algebra representations could be generalized and extended to other algebras such as groups and rings. While I still don't have a satisfying grasp on the topic, I realized that this topic is one of the most interesting ones that I have studied so far!
No comments:
Post a Comment