# Questions tagged [differential-graded-algebras]

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### DG-Modules over CDG-algebras in the sense of rational homotopy theory.

Suppose we have a rationalization $\bar{X}$ of a simply connected topological space $X$. Then we can construct a CDG-algebra - a Sullivan model $S$ corresponding to $\bar{X}$. How can we interpret ...
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### $A$ - dga over field, then $H^i(A) = 0, i > 1$ implies $HH_i(A) = 0, i < -1$

Let $(A,d)$ - dg-algebra with unit over field $k$ such that $H^i(A) = 0$ for $i > 1$, then $HH_i(A) = 0, i < -1$. I prove that using bar resolution, fact that cohomology commutes with filtered ...
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### Why aren't there any derivations of degree inferior to $-1$ of the DG-algebra $(\Omega(A), d_A, \wedge)$?

Let $A$ be a vector bundle over a manifold $M$. We can assotiate a graded algebra $(\Omega(A), \wedge)$ where $$\wedge:\Omega^i(A)\times \Omega^j(A)\longrightarrow \Omega^{i+j}(A),$$ is given by (\...
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### Definition of $\mathfrak{g}$-differential graded algebra

I am reading Group actions on manifolds by Eckhard Meinrenken (Lecture Notes, University of Toronto, Spring 2003). In page $45$, definition $5.2$, author introduce the notion of $\mathfrak{g}$-...
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### A condition for a dga to be minimal

I'm reading a book "Complex Geometry" by Daniel Huybrechts. In this book he says that a simply connected dga satisfying some conditions must be minimal. (p.147, Remark 3.A.13) I tried to prove this ...
### if $C$ is a filtered coalgebra, does Gr($B\Omega C)\backsimeq B\Omega ($Gr $C)$ hold?
I have heard that under some assumptions, the functor 'Gr' from filtered graded objects with exhaustive filtration to graded objects $X\rightarrow$ Gr$(X)$ commutes with direct sums (this seems to be ...
### When does a fibration $f:X\rightarrow Y$ in a model category admit a section?.
If we have a fibration $f:X\rightarrow Y$ in a model category $C$, where $Y$ is cofibrant and both $X, Y$ are fibrant. Does f admit a section (right inverse)?. If it does not work in general, ...