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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

On the homotopy of simplicial algebras
over an operad


Author: Benoit Fresse
Journal: Trans. Amer. Math. Soc. 352 (2000), 4113-4141
MSC (1991): Primary 18C15, 18G30; Secondary 55S99, 55U10
Published electronically: October 5, 1999
MathSciNet review: 1665330
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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.


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Additional Information

Benoit Fresse
Affiliation: Laboratoire J.A. Dieudonné, Université de Nice, Parc Valrose, F-06108 Nice Cedex 02, France
Email: fresse@math.unice.fr

DOI: http://dx.doi.org/10.1090/S0002-9947-99-02489-7
PII: S 0002-9947(99)02489-7
Received by editor(s): February 17, 1998
Published electronically: October 5, 1999
Article copyright: © Copyright 2000 American Mathematical Society