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arXiv · 1904.07352

Deformation Theory and Partition Lie Algebras

Lukas Brantner·Akhil Mathew
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Abstract

A theorem of Lurie and Pridham establishes a correspondence between formal moduli problems and differential graded Lie algebras in characteristic zero, thereby formalising a well-known principle in deformation theory. We introduce a variant of differential graded Lie algebras, called partition Lie algebras, in arbitrary characteristic. We then explicitly compute the homotopy groups of free algebras, which parametrise operations. Finally, we prove generalisations of the Lurie-Pridham correspondence classifying formal moduli problems via partition Lie algebras over an arbitrary field, as well as over a complete local base.

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Lukas Brantner, Akhil Mathew. 2019-04-15. Deformation Theory and Partition Lie Algebras. https://arxiv.org/abs/1904.07352

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