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<p>We show that there is an equivalence of <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\infty \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>∞</mi> </math></EquationSource> </InlineEquation>-categories between Lie algebroids and certain kinds of curved Lie algebras. For this we develop a method to study the <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\infty \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>∞</mi> </math></EquationSource> </InlineEquation>-category of curved Lie algebras using the homotopy theory of algebras over a complete operad.</p>

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Lie algebroids are curved Lie algebras

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年6月29日

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  • Damien Calaque,
  • Ricardo Campos,
  • Joost Nuiten

摘要

We show that there is an equivalence of \(\infty \) ∞ -categories between Lie algebroids and certain kinds of curved Lie algebras. For this we develop a method to study the \(\infty \) ∞ -category of curved Lie algebras using the homotopy theory of algebras over a complete operad.