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6
votes
2answers
435 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
2answers
163 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
1answer
281 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 ...