| Topic | People | Description |
|---|---|---|
| Purity in representation theory |
Lidia Angeleri
Rosanna Davison Laking |
The theory of purity incorporates the study of pure-injective modules, definable subcategories and the Ziegler spectrum. Pure-injective modules are those that have a particular "compactness" property with respect to infinite systems of linear equations. Such modules play an important role in the model theory of modules, approximation theory and generalisations of Auslander-Reiten theory. The techniques involved can be extended to triangulated categories via categories of functors. |
| Representation theory of algebras |
Lidia Angeleri
Georgios Dalezios Rosanna Davison Laking Francesca Mantese |
Representation theory studies rings and algebras in terms of their representations, that is, by investigating the associated module categories and their derived categories. One of the main goals is to understand the complexity of these categories. Particular attention is devoted to finite dimensional algebras over a field and to the role played by infinite dimensional modules over such algebras. |
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