Maurer-Cartan spaces of filtered L-infinity algebras

Sinan Yalin (1)

1 FSTC - Faculty of Science, Technology and Communication [Luxembourg]

We study several homotopical and geometric properties of Maurer-Cartan spaces for L-infinity algebras which are not nilpotent, but only filtered in a suitable way. Such algebras play a key role especially in the deformation theory of algebraic structures. In particular, we prove that the Maurer-Cartan simplicial set preserves fibrations and quasi-isomorphisms. Then we present an algebraic geometry viewpoint on Maurer-Cartan moduli sets, and we compute the tangent complex of the associated algebraic stack.

Mots clés: Lie algebras; Maurer-Cartan simplicial sets; deformation theory; stacks

Domaines: Topologie algébrique [math.AT]; Géométrie algébrique [math.AG]

Sinan Yalin. Maurer-Cartan spaces of filtered L-infinity algebras. Journal of Homotopy and Related Structures, 2016, 11 (3), pp.375-407. ⟨hal-01064418⟩