All Questions
Tagged with a-infinity-algebras homotopy-theory
9 questions with no upvoted or accepted answers
10
votes
0
answers
292
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Formulation of $A_\infty$ structures in terms of coalgebras
There are two ways to define $A_\infty$ structures. The elementary one seems rather intuitive when I think of higher homotopies. I.e. an $A_\infty$ structure on a $\mathbb{Z}$-graded vector $A$ space ...
10
votes
0
answers
268
views
Isomorphisms between minimal $A_\infty$-algebras having identical $k$-truncations
Let $A_m =(A,0,m_2,m_3,\dots)$ and $A_n=(A,0,n_2,n_3,\dots)$ be two $A_\infty$-structures on a vector space $A$. Assume that
i) $A_m$ and $A_n$ are isomorphic, and
ii) $A_m$ and $A_n$ have the same ...
- 523
4
votes
0
answers
96
views
Transferring $A_\infty$-structure from a module to its homology
Given an $A_\infty$-module $M$, which is a graded module $M=\bigoplus_{k\in\mathbb{Z}}M_k$ with morphisms $m_n^M\colon A^{\otimes(n-1)}\otimes M\rightarrow M$ of degree 2-n satisfying the $A_\infty$ ...
- 213
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
3
votes
0
answers
150
views
Strict units in A-infinity algebras
In Kontsevich-Soibelman's paper "Notes on $A_\infty$-algebras, $A_\infty$-categories and non-commutative geometry", $A_\infty$-algebras with strict units are defined so units act trivially on higher ...
- 1,975
3
votes
0
answers
256
views
Tensor product of $A_{\infty}$ algebra morphisms, reference
Let $\Bbbk$ be a field of charachteristic zero. Let $(A, m_{\bullet}^{A})$ be an unital $A_{\infty}$ algebra. Let $B$ be a differential graded algebra. Then $B\otimes A$ carries an $A_{\infty}$ ...
- 1,424
3
votes
0
answers
476
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(co)chain homotopy of dg algebras ($A_{\infty}$ algebras) and other notion of homotopy
In this question I will work over a field of char. $0$. Let $f,g\: : \: A\to B$ be dg algebras morphism between two cochain (commutative) dg algebras $A,B$ (assume positively graded). Let $h$ be a ...
- 1,424
2
votes
0
answers
102
views
Does the totality of $E_n$-operads in a given category has any interesting structure?
Suppose we are given a fixed ambient symmetric monoidal model category (I'm mostly interested in chain complexes over char zero fields). Then we have the notion of an $E_n$-operad in that category. ...
- 2,074
1
vote
0
answers
167
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Khovanov $A_\infty$ algebra
Let $L$ be a link in $\mathbb{R}^3$, with $D, D'$ be diagrams in
$\mathbb{R}^2$ representing $L$. Khovanov constructed two graded
chain complexes $$C_{D} = (Ch_{D}, d_{D}) \quad C_{D'}=(Ch_{D'},
d_{D'}...
- 5,230