All Questions
Tagged with quivers triangulated-categories
4
questions
16
votes
0
answers
422
views
Is there a cotangent bundle of a stable $\infty$-category?
Let $C$ be a stable $\infty$-category. Is there any categorical construction $C \mapsto T^* C$, where $T^* C$ is another stable $\infty$-category, that specializes to the following?
When $C$ is the ...
- 4,819
13
votes
0
answers
604
views
The derived category of integral representations of a Dynkin quiver
Let $Q$ be a Dynkin quiver. Let $\mathbb CQ$ be its complex path algebra. It is defined in a way such that modules over $\mathbb CQ$ are the same as representations of the quiver $Q$. Let's write $\...
- 3,114
3
votes
0
answers
95
views
Mutations in triangulated category and cluster algebra
Let $\mathcal{D}$ be an enhanced triangulated category (basically meaning that $\operatorname{Hom}$'s are complexes). There is the notion of mutation in an enhanced triangulated category: given a full ...
- 945
2
votes
0
answers
142
views
An equivalence between projective modules over the preprojective algebra and an orbit category
Let $Q$ be a Dynkin quiver, and let $kQ$ be its path algebra over some field k. Let $\Pi$ be the preprojective algebra of $Q$. Then (c.f. Section 7.3 of Keller's On Triangulated Orbit Categories) the ...
- 217