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### Maurer-Cartan equation for Lie groups/homogeneous space vs. Maurer-Cartan of deformation theory

What is the relationship between the Maurer-Cartan equation
$$
d\theta + \dfrac{1}{2}[\theta,\theta] = 0
$$
satisfied by Maurer-Cartan forms on Lie groups, or by pullbacks of Maurer-Cartan forms along ...

**6**

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**2**answers

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### Higher commutators in E_n algebras and the Maurer--Cartan equation

Let $A$ be an associative algebra in $dgVect_k$. Then the commutator $[\cdot,\cdot]:A\otimes A\to A$ defined by $[x,y]=xy-(-1)^{|x||y|}yx$ gives $A$ the structure of a (dg-)Lie algebra. The Maurer--...

**1**

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### tensor hierarchy for Lie groups from Maurer-Cartan form

The question is about the family of tensors that are naturally associated to any nice Lie group.
Take the Mauer-Cartan form, $\omega=g^{-1} dg$ and I would like to make the covariant index of this one-...

**3**

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**1**answer

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### Do the solutions of the Maurer--Cartan equation form a simplicial set?

The Maurer--Cartan equation is the equation:
$$d\gamma+\frac 12[\gamma,\gamma]=0$$
where $\gamma$ represents a degree one element in a differential graded Lie algebra $\mathfrak g^\ast$. Let's denote ...