| Abstract: |
| D. Happel introduced the root category as a two-periodic orbit triangulated category R of the derived category of Dynkin quiver. The Gabriel Theorem can be stated with the Auslander-Reiten quiver of R, not only for the positive roots $\Phi^+$ but also the whole root system Phi. We introduce here a process to build up semi-simple Lie algebras and Chevalley groups via Hall algebra approach. The construction can be applied to a realization of compact real form and maximal compact subgroups from the root category R, and obtain the Peter-Weyl Theorem and the Plancherel Theorem for compact groups. This is a joint work with Buyan Li. |
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