In
1963, Gerstenhaber invented an operad calculus in the Hochschild complex of an
associative algebra; operads were introduced under the name of pre-Lie systems.
In the same year, Stasheff constructed quite an original geometrical operad, which nowadays is called an associahedra. The notion of an operad was further
formalised by May as a tool for iterated loop spaces. The main principles of
the operad calculus (brace algebra) were presented by Gerstenhaber and Voronov.
Some quite remarkable research activity in the operad theory and its
applications can be observed in the last decade. It may be said that operads
are also becoming an important tool for Quantum Field Theory and deformation
quantization.
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