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Transactions of the American Mathematical Society
Journal Article

On the Homotopy of Simplicial Algebras over an Operad

Benoit Fresse
Transactions of the American Mathematical Society
Vol. 352, No. 9 (Sep., 2000), pp. 4113-4141
Published by: American Mathematical Society
https://www.jstor.org/stable/118177
Page Count: 29

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Topics: Functors, Monads, Tensors, Commutativity, Mathematical theorems, Polynomials, Distributivity
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On the Homotopy of Simplicial Algebras over an Operad
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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.
Transactions of the American Mathematical Society © 2000 American Mathematical Society