10:30 - 5:00
Today I explored the specific structure of Sl2(C), the set of 2x2 matrices of complex numbers whose diagonal elements add up to 0. I learned about a very cool and intricate theorem, which used a basis of that Lie algebra to classify any irreducible module. While reading about this, I thought about how these irreducible modules act as Lego pieces, which look boring by themselves but can be fit together to yield very cool and complicated structures.
Because this theorem was very hard to conceptualize, I had to spend a lot of time on this chapter, and unfortunately I was not able to finish the exercises available. However, I was able to fully grasp this specific theorem, which the author contends has tremendous amounts of applications and possible generalizations. I can't wait to find out more!
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