On the homotopy of simplicial algebras over an operad

Fresse, Benoit

doi:10.1090/S0002-9947-99-02489-7

On the homotopy of simplicial algebras over an operad
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Trans. Amer. Math. Soc. 352 (2000), 4113-4141 Request permission

Abstract:

According to a result of H. Cartan, the homotopy of a simplicial commutative algebra is equipped with divided power operations. In this article, we show how to extend this result to other kinds of algebras. For instance, we prove that the homotopy of a simplicial Lie algebra is equipped with the structure of a restricted Lie algebra.

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