All Questions
Tagged with a-infinity-algebras reference-request
7 questions with no upvoted or accepted answers
7
votes
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244
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Operad-free proofs of rectification of homotopy ($A_\infty/L_\infty$) algebras?
If (say) $L$ is an $L_\infty$-algebra, then it is known that under certain conditions there exists a quasi-isomorphic $L_\infty$-algebra $L'$ which is a differential graded Lie algebra: all ternary ...
- 784
5
votes
0
answers
303
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Recovering an A-infinity structure on an Ext-algebra from a quiver presentation
Let $A=KQ/I$ be a basic finite dimensional algebra given by a quiver with relations. Let $S$ denote the direct sum of the corresponding simple modules.
According to [Keller: A-infinity algebras in ...
- 2,450
5
votes
0
answers
151
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$A_\infty$ structure on sum of twists of structure sheaf
Fix $n$ and let $P^n$ be projective $n$-space. Let $S = k[x_0, \dots, x_n]$. Set $A^0 = \bigoplus_{d \ge 0} H^0(P^n, \mathcal{O}(d))$ and $A^n = \bigoplus_{d < -n} H^n(P^n, \mathcal{O}(d))$.
I ...
- 10.7k
4
votes
0
answers
126
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Minimal model for $A_\infty$-categories
Is there a reference for existence and construction of the minimal model of an $A_\infty$-category? Most references I found ultimately refer to Lefèvre-Hasegawa's thesis but there doesn't seem to be a ...
- 489
4
votes
0
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225
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Natural transformations of $A_\infty$-functors (between dg-categories) are "directed homotopies" (reference?)
Let $\mathbf A$ and $\mathbf B$ be dg-categories over a field, viewed as $A_\infty$-categories. The $A_\infty$-category (actually, dg-category) of strictly unital $A_\infty$-functors $\mathbf A \to \...
- 2,079
3
votes
0
answers
261
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On the Hochschild cohomology of the minimal model of an $A_\infty$ algebra
Suppose $(A, (\mu_k))$ is a (curved) $A_\infty$ algebra, and let $(\tilde A, (\tilde\mu_k))$ be its minimal model. Now, we have two Hochschild cohomology rings $HH^*(A)$ and $HH^*(\tilde A)$. (It may ...
- 2,789
1
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79
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Reference request for showing open(resp. closed) string field theory has A-infinity(resp. L-infinity) algebra structure
I've now begun to study about the relationship between open(resp. closed) string field theory and A-infinity(resp. L-infinity) algebra structure.
For the A-infinity case, I'd already heard that the ...
- 285