Homotopy Algebras via Resolutions of Operads

Abstract

The aim of this brief note is mainly to advocate our approach to homotopy algebras based on the minimal model of an operad. Our exposition is motivated by two examples which we discuss very explicitly - the example of strongly homotopy associative algebras and the example of strongly homotopy Lie algebras. We then indicate what must be proved in order to show that these homotopy algebraic structures are really `stable under a homotopy.' The paper is based on a talk given by the author on June 16, 1998, at University of Osnabrueck, Germany.

arXiv commentLaTeX 2.09, 9 pages; `indecomposables' changed to `decomposables'

References in corpus (2)

• Introduction to sh Lie algebras for physicists
• The sh Lie structure of Poisson brackets in field theory

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• Higher derived brackets, strong homotopy associative algebras and Loday pairs
• Natural differential operators and graph complexes