Questions tagged [differential-graded-lie-algebras]
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8 questions
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What is the DGLA controlling deformations of a group representation?
Fix a (discrete) group $G$, characteristic zero field $k$ and representation $\rho_0: G \to \mathrm{GL}_n(k)$. I want to consider the formal deformations of $\rho_0$.
My understanding is there is a ...
- 61
2
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"smooth transition" from differential graded Lie algebra to $L_\infty$-algebras
Question is as in the title.
When learning about $L_\infty$-algebras for the first time, is there a "smooth transition" one can make from differential graded Lie algebras to $L_\infty$-...
- 6,023
8
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416
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Conceptual explanation for the sign in front of some binary operations
In several situations, I've seen that given a binary operation on a graded module $m:A\otimes A\to A$, a new operation $M(x,y)=(-1)^{|x|}m(x,y)$ is defined so that it satisfies some properties.
One ...
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5
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1
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Graded commutativity of the $n$th Browder bracket
Let $\mathcal{O}$ be a topological operad and $X$ an algebra over $\mathcal{O}$. Then $H_*(X)$ is an algebra (in the category of $\mathbb{Z}$-graded $R$-modules) over $H_*(\mathcal{O})$. Each $e\in ...
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3
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A question about the definition of complete dg Lie algebras in a paper of Lazarev and Markl
In their paper Disconnected Rational Homotopy Theory, Lazarev and Markl give the following definition (page 23):
Definition: A complete differential graded Lie algebra is an inverse limit of finite-...
1
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186
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Differential graded Lie algebras and gauge equivalent
For the Kodaira-Spencer complex $\Omega^{0,*}(T^{1,0})[[t]]$ on a compact complex manifold, with a Hermitian metric. It is well known that finding formal series solution $\Xi = \Xi_1 t^1 + \Xi_2 t^2 + ...
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Invariant definition of graded Poisson bracket
Given a graded manifold with symplectic form $\omega$ of degree $n$, I have seen two expressions for the corresponding Poisson bracket of degree $-n$. Cattaneo-Fiorenza-Longoni, http://www.math.uzh.ch/...
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Model category structures on the category of $L_\infty$-algebras
Let $k$ be a characteristic zero field. Then it is known that the forgetful functor $dgla(k)\to chain(k)$ from differential graded Lie algebras (over $k$) to cochain complexes induces a model category ...
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