# Tagged Questions

**3**

votes

**1**answer

99 views

### A canonical algebra of type $(2,2,r)$ is derived equivalent to a path algebra of type $\tilde{D}_{r+2}$ (references)

According to several articles I could find, a canonical algebra of type $(2,2,r)$ is derived equivalent to a path algebra of type $\tilde{D}_{r+2}$, where $r \geq 2$.
I don't know how to obtain this ...

**5**

votes

**1**answer

182 views

### Equivariant Formality

Let $G$ be a finite group and $\mathcal{A}$ be a $dg$-algebra. Assume $G$ acts on $\mathcal{A}$, i.e. there exists a homomorphism $G\to {\rm Aut}_{dg}(\mathcal{A})$.
Assume further there exists a ...

**0**

votes

**0**answers

246 views

### generators for derived category

Let $G$ be a algabraic group $G$ over a field $k$. We denote by $D^b(\mathrm{Repr}(G))$ the derived category of finite dimensional representations. Under what kind of assmumptions one has a generating ...

**10**

votes

**0**answers

367 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 ...

**5**

votes

**1**answer

386 views

### Generators of the derived category

For a ring $R$, which is a finite-dimensional algebra over a field, the category of finite-dimensional, projective, right $R$-modules, $\mathcal{P}_R$ is generated by the indecomposable projective ...

**2**

votes

**3**answers

691 views

### Exceptional collections with many Exts

Background definitions:
Let $D$ be a triangulated category arising in nature (for instance as the cohomology category of a dg category). An object $E$ in $D$ is called exceptional if $RHom(E,E)$ is ...

**7**

votes

**3**answers

703 views

### Are the underlying undirected graphs of two mutation-equivalent acylic quivers isomorphic?

Quiver mutation, defined by Fomin and Zelevinsky, is a combinatorial process. It is important in the representation theory of quivers, in the theory of cluster algebras, and in physics.
We consider ...

**5**

votes

**2**answers

586 views

### What is the geometric meaning of reconstruction of quantum group via Ringel Hall algebra

If I remembered correctly. There are some work done by C.M.Ringel,he defined so called Ringel-Hall algebra on abelian category and then show that Ringel-hall algebra is isomorphic to positive part of ...

**7**

votes

**3**answers

686 views

### Compact generation for modular representations

Are the derived categories of modular representations of algebraic groups compactly generated? (e.g. consider SL_2 in characteristic 2). Note modular reps of finite groups are compactly generated (by ...