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ag.algebraic geometry – Road map: past Artin-Wedderburn theorem

For a noncommutative semisimple ring $R$, its construction and its class of representations can breathe largely understood utilizing Artin-Wedderburn theorem. Such construction concept is helpful, for instance, within the complicated illustration concept of finite teams $G$.

Every from time to time, I encountered rings whose constructions are extra lax. For instance, $mathbb{F}[G]$, the place the bailiwick is not a pleasant as $mathbb{C}$. Another instance is the Borel-Moore homology $H(Z;mathbb{C})$ of the Steinberg selection $Z$, which by Deligne’s decomposition theorem is semisimple modulo its nilradical [1, (8.6.11)].

I thus want to increase my information past A-W theorem, however I’m too cognizant that the idea might breathe much less organized. Would you intellect offering some pointers, or plane higher a street map? It’d breathe noble if the summary concept is conduct with some functions to vital works love the above.

### Reference

- [1] Representation concept and Complex Geometry by Chriss and Ginzburg.

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