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To each minimal Sullivan algebra \(\land V\) is associated with an enriched Lie algebra \(L_V\) , isomorphic to the homotopy Lie algebra of the geometric realization \(\langle \land V\rangle \) of \(\land V\) . When \(\land V\) is the minimal model of a connected spaceX, then \(\langle \land V\rangle \) is the rationalization \(X_{\mathbb Q}\) ofX, and \(L_V\) is denoted by \(L_X\) . We present the first properties of \(L_V\) and describe \(L_X\) in the case of a wedge of spaces.

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The Homotopy Lie Algebra \(L_V\) of a Minimal Sullivan Algebra

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  • 发表日期：

    2026年

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  • Yves Félix,
  • Steve Halperin

摘要

To each minimal Sullivan algebra \(\land V\) is associated with an enriched Lie algebra \(L_V\) , isomorphic to the homotopy Lie algebra of the geometric realization \(\langle \land V\rangle \) of \(\land V\) . When \(\land V\) is the minimal model of a connected spaceX, then \(\langle \land V\rangle \) is the rationalization \(X_{\mathbb Q}\) ofX, and \(L_V\) is denoted by \(L_X\) . We present the first properties of \(L_V\) and describe \(L_X\) in the case of a wedge of spaces.