Related papers: Some problems in operad theory
This is an expository article about operads in homotopy theory written as a chapter for an upcoming book. It concentrates on what the author views as the basic topics in the homotopy theory of operadic algebras: the definition of operads,…
This is a cornucopia of types of algebras with some of their properties from the operadic point of view.
I exhibit a pair of non-symmetric operads that, although not themselves isomorphic, induce isomorphic monads. The existence of such a pair implies that if `algebraic theory' is understood as meaning `monad', operads cannot be regarded as…
We review definitions and basic properties of operads, PROPs and algebras over these structures.
This survey provides an elementary introduction to operads and to their applications in homotopical algebra. The aim is to explain how the notion of an operad was prompted by the necessity to have an algebraic object which encodes higher…
In this article, we describe how coalgebraic structures on operads induce algebraic structures on their categories of algebras and coalgebras.
Operads are algebraic devices offering a formalization of the concept of operations with several inputs and one output. Such operations can be naturally composed to form bigger and more complex ones. Coming historically from algebraic…
The theory of operads (May, cyclic, modular, PROPs, etc) is extended to include higher dimensional phenomena, i.e. operations between operations, mimicking the algebraic structure on varieties of arbitrary dimensions, having marked…
The essential parts of the operad algebra are concisely presented, which should be useful when confronting with the operadic physics. It is also clarified how the Gerstenhaber algebras can be associated with the linear pre-operads (comp…
We present a treasure trove of open problems in matrix and operator inequalities, of a functional analytic nature, and with various degrees of hardness.
The aim of this paper is to present remarkable classes of Lie-admissible algebras containing in particular the associative algebras, the Vinberg algebras and pre-Lie algebras. We determine the associated quadratic operads and their dual…
In this note devoted to some aspects of the inverse problem of representation theory the attention is concentrated on the interrelations between various algebraic structures (algebras with operators) unraveled by different solutions of the…
It is clarified how cohomologies and Gerstenhaber algebras can be associated with linear pre-operads (comp algebras). Their relation to mechanics and operadic physics is concisely discussed.
We generalize the construction of multitildes in the aim to provide multitilde operators for regular languages. We show that the underliying algebraic structure involves the action of some operads. An operad is an algebraic structure that…
We develop deformation theory of algebras over quadratic operads where the parameter space is a commutative local algebra. We also give a construction of a distinguised deformation of an algebra over a quadratic operad with a complete local…
An operad describes a category of algebras and a (co)homology theory for these algebras may be formulated using the homological algebra of operads. A morphism of operads $f:\mathcal{O}\rightarrow\mathcal{P}$ describes a functor allowing a…
The paper surveys various Waring type problems in groups, Lie algebras, and associative algebras.
A general notion of operad is given, which includes as instances, the operads originally conceived to study loop spaces, as well as the higher operads that arise in the globular approach to higher dimensional algebra. In the framework of…
In this exposition, I discuss several developments in the theory of vertex operator algebras, and I include motivation for the definition.
In this note we briefly survey and propose some open problems related to isoparametric theory.