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Results tagged with rt.representation-theory
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user 5323
Linear representations of algebras and groups, Lie theory, associative algebras, multilinear algebra.
7
votes
3
answers
635
views
Do Denominator Vectors Determine the Cluster Variable
Given a cluster algebra $A=A(\mathbf{x},Q)$, the Laurent Phenomenon states that all the cluster variables of $A$ are Laurent polynomials in the elements of $\mathbf{x}$. Thus, any cluster variable $y …
- 2,283
1
vote
Accepted
An algorithm for constructing the AR-quiver of a path algebra corresponding to a change in t...
The algorithm for constructing the AR-quiver of any orientation of $A_n$ is the same as the algorithm for constructing the AR-quiver of the orientation you describe. Start out by figuring out all the …
- 2,283
9
votes
3
answers
625
views
Group Extensions and Line Bundles on $BG$
I am sure the answer to this question is well-known, but
It is well known that the group cohomology $H^2(G,\mathbb Z)$ classifies group extensions $0\to \mathbb Z\to E\to G\to 1$ and that for a topo …
- 2,283
17
votes
2
answers
2k
views
Which cluster algebras have been categorified?
In "Tilting Theory and Cluster Combinatorics" Buan, Marsh, Reineke, Reiten, and Todorov constructed cluster categories for mutation finite cluster algebras (without coefficients), and Amiot gives a co …
- 2,283
18
votes
1
answer
1k
views
Homology in the $A_\infty$ World
This question is turning out to be a little long so let me start off with the headline. Given a differential graded algebra $A$, we can recover $A$ from its homology $HA$ if we know "the" $A_\infty$- …
- 2,283