ABSTRACT
One of the main reasons to study associative algebras is the notion of a module over an associative algebra, that is a vector space where an algebra acts by endomorphisms. Similarly, when talking about some class of algebras, e.g., associative algebras, Lie algebras, Jordan algebras, etc., it is useful to consider the collection of all operations with several arguments made of structure operations on this algebra, and study algebraic structures of that collection. This leads naturally to various notions of an operad. Sergei Merkulov [196] came up with a beautiful analogy for that: similar to how the Cheshire Cat from Alice’s Adventures in Wonderland tends to disappear almost completely so that the only thing left is the cat’s grin, an operad is a “grin of an algebra”, that is what remains when we take an algebra, that is a vector space with structure operations, and remove the vector space.
