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Journal of Homotopy and Related Structures

, Volume 11, Issue 3, pp 375–407 | Cite as

Maurer–Cartan spaces of filtered \(L_{\infty }\)-algebras

  • Sinan Yalin
Article

Abstract

We study several homotopical and geometric properties of Maurer–Cartan spaces for \(L_{\infty }\)-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.

Notes

Acknowledgments

I would like to thank Gennaro di Brino and Bertrand Toen for useful discussions about stacks.

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Copyright information

© Tbilisi Centre for Mathematical Sciences 2015

Authors and Affiliations

  1. 1.Mathematics Research UnitUniversity of LuxembourgLuxembourgLuxembourg

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