Due to the delayed start last week, we were unable to hold the scheduled Ulam lecture. Breeann will thus speak during the problem session time slot (Tuesday 4:05-4:55pm) on representations of sl(2,C) and sl(3,C). On Thursday, Mike will discuss the representations of g_2.
Note that beginning next week, we will start on the notes of Steinberg on Chevalley groups. These can be purchased during the month of February through the AMS for a discounted price of just under $20.
The root decomposition and representation theory of the exceptional Lie algebra g_2
Feb. 24, 2022 2:30pm (MATH 3…
Functional Analysis
Levi Lorenzo (CU Boulder)
X
As we continue our discussion of analytic K-homology, we encounter Fredholm modules in a motivating example. As seen, operator algebras allow us to recover topological spaces in the noncommutative setting, and K-homology is a valuable invariant for these noncommutative spaces. This week, we look at spaces with additional structure and attempt to recover that structure as algebraic data. Namely, if we have a manifold with a (smooth, Riemannian, Spin, Spin^c) structure, we port that information into the noncommutative world using Spectral Triples. We see how Spectral Triples open the doors to the calculus of noncommutative spaces and how a Spectral Triple determines the topological data of a space in the form of a Fredholm module and a class in K-homology.