All Questions
7 questions
10
votes
1
answer
1k
views
What's the relationship between spherical twist functors and tilting?
I've been reading about connections between Coxeter groups and preprojective algebras, and I keep running into two operations on the derived categories of preprojective algebras which seem very ...
- 453
6
votes
1
answer
775
views
Socle of tilting modules in the BGG category $\mathcal{O}$ over a semisimple Lie algebra
Suppose that $\mathfrak{g}$ is a finite dimensional, complex, semisimple Lie algebra. Let $\mathcal{O}$ be the BGG category over $\mathfrak{g}$.
Tilting module theory play an important role in the ...
- 159
5
votes
1
answer
212
views
On tilting and cotilting modules
Let A be an Artin algebra and assume all modules are basic, then a classical result says that tilting modules $T$ are in bijection with complete cotorsion pairs $(T^{\perp}, \check{ add(T)})$ (with ...
- 26.5k
2
votes
0
answers
47
views
Is a triangulated category admitting a tilting object triangle equivalent to the unbounded derived category of the endomorphism ring of this object?
Let $\mathcal{T}$ be a triangulated category. We call an object $G$ tilting if
$G$ is compact, that is, $\mathrm{Hom}_{\mathcal{T}}(G, -)$ preserves all set-indexed coproducts;
$G$ is a generator, ...
- 21
2
votes
1
answer
213
views
How to get $Hom_A(M,N) \cong Hom_{B^{op}}(Hom_A(N,T),Hom_A(M,T))$?
I am reading the paper"Dominant dimensions, derived quivalences and tilting modules", the link is here:http://link.springer.com/article/10.1007/s11856-016-1327-4.
On page 22,Lemma 4.2 says that let M ...
- 775
2
votes
0
answers
203
views
Could Partial Tiltings be studied as Almost Complete Tiltings?
The first part of what follows is a brief recap of the definitions, setting and motivations for my questions. Experts can find the questions at the end.
Here $k$ denotes an algebraically closed field,...
- 493
1
vote
1
answer
215
views
The projective modules of an algebra and the tilting module?
Let A be an algebra. We denote by by A-proj the full subcategory of A-mod consisting of projective modules. An A-module T is called a tilting module if $proj.dim(_{A}T)=n < \infty$, $Ext_{A} ^{j} (...
- 775