The maurer-cartan-equation tag has no usage guidance.

**6**

votes

**2**answers

519 views

### 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 ...

**1**

vote

**2**answers

189 views

### 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 ...

**3**

votes

**1**answer

390 views

### 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 ...