Everything about Operad
Generalization of associativity properties
In mathematics, an operad is a structure that consists of abstract operations, each one having a fixed finite number of inputs (arguments) and one output, as well as a specification of how to compose these operations. Given an operad, one defines an algebra over to be a set together with concrete operations on this set that behave just like the abstract operations of. For instance, there is a Lie operad such that the algebras over are precisely the Lie algebras; in a sense abstractly encodes the operations that are common to all Lie algebras. An operad is to its algebras as a group is to its group actions. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: OperadA 5-minute orientation
- Skim a recent paper: The minimal model of Rota-Baxter operad with arbitrary weightInfluential work since 2022
- Pick up a classic book: Algebraic operadsThe most-reprinted book on the subject
- Read the landmark paper: Combinatorial operad actions on cochainsCited 92 times
- Go sideways: A∞-operadA closely related topic
- Go sideways: E∞-operadA closely related topic
📖 Definitions
Noun A set of operations, each one having a fixed finite number of arguments and one output, which can be composed with others.
🏆 Landmark papers (most cited)
Combinatorial operad actions on cochains
Formality of Chain Operad of Little Discs
On operad structures of moduli spaces and string theory
Character formulas for the operad of two compatible brackets and for the bi-Hamiltonian operad
On the operad of associative algebras with derivation
On the homotopy of simplicial algebras over an operad
The minimal model for the Batalin–Vilkovisky operad
Codimension Growth and Non-Koszulity of Novikov Operad
🆕 Influential since 2022
The minimal model of Rota-Baxter operad with arbitrary weight
Cohomology and deformation theory for operad with higher derivation
A cell decomposition of the Fulton MacPherson operad
Projective and Reedy Model Category Structures for (Infinitesimal) Bimodules over an Operad
On the Dong Property for a binary quadratic operad
📚 Books worth reading
- 📕Algebraic operadsMurray R. Bremner · 2016
Higher Operads, Higher CategoriesTom Leinster · 2004- 📕Generalized bialgebras and triples of operadsJean-Louis Loday · 2008
- 📕Formality of the little N-disks operadPascal Lambrechts · 2014
Woods Hole mathematicsR. C. Penner · 2004- 📕Operads 2009Jean-Louis Loday, Bruno Vallette · 2013
Modules over operads and functorsBenoit Fresse · 2009- 📕Operads and chain rules for the calculus of functorsGregory Arone · 2011
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
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