In many areas of mathematics some “higher operations” are arising. These havebecome so
important that several research projects refer to such expressions. Higher operationsform …

Operads are mathematical devices that describe algebraic structures of many varieties and
in various categories. Operads are particularly important in categories with a good notion of …

We give a construction of homotopy algebras based on “higher derived brackets”. More
precisely, the data include a Lie superalgebra with a projector on an Abelian subalgebra …

In the present paper we develop the deformation theory of operads and algebras over
operads. Free resolutions (constructed via Boardman-Vogt approach) are used in order to …

This book gives a thorough and self-contained introduction to the theory of Hochschild
cohomology for algebras and includes many examples and exercises. The book then …

In this paper and its follow-up [Merkulov and Vallette, J. reine angew. Math.], we study the
deformation theory of morphisms of properads and props thereby extending Quillen's …

In this paper we construct a small $ E_\infty $ chain operad $\mathcal {S} $ which acts
naturally on the normalized cochains $ S^* X $ of a topological space. We also construct, for …

By exploiting the BV quantization of topological bosonic open membrane, we argue that flat
3-form C-field leads to deformations of the algebras of multi-vectors on the Dirichlet-brane …

Galois explained to us that operations acting on the solutions of algebraic equations are
mathematical objects as well. The notion of an operad was created in order to have a well …

We prove that strongly homotopy algebras (such as Ay, Cy, sh Lie, Gy,...) are homotopy
invariant concepts in the category of chain complexes. An important consequence is a …