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In the representation theory of semisimple Lie algebras, Category O (or category O {\displaystyle {\mathcal {O}}} ) is a category whose objects are certain representations of a semisimple Lie algebra, and whose morphisms are homomorphisms of representations.
Basic properties, Koszul duality & Examples
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displaystyle mathcal category koszul mathfrak algebra finite-dimensional graded block duality mathrm gr text semisimple lie algebras objects representations generated module
| Subject | Predicate | Object | Confidence | Src |
|---|---|---|---|---|
| the geometry of the flag variety | instance of | is closely connected with geometric and combinatorial structures | 0.80 | text |
| perverse sheaves | instance of | is closely connected with geometric and combinatorial structures | 0.80 | text |
| and Kazhdan | instance of | is closely connected with geometric and combinatorial structures | 0.80 | text |
| Category O | related to Basic properties | Each | 0.60 | section |
| Category O | related to Basic properties | Noetherian | 0.60 | section |
| Category O | related to Basic properties | Objects | 0.60 | section |
| Category O | related to Definition of category O | The | 0.60 | section |
| Category O | related to Examples | All | 0.60 | section |
| Category O | related to Examples | Verma | 0.60 | section |
| Category O | related to Koszul duality | Koszul | 0.60 | section |
| Category O | related to Koszul duality | In | 0.60 | section |
| Category O | related to Koszul duality | Beilinson | 0.60 | section |
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