Related papers: Families of algebraic 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…

We aim at studying collections of algebraic structures defined over a commutative ring and investigating the complexity of significant constructions carried out on these objects. The assignment of measures of size, via a multiplicity…

We describe a framework for systematic enumeration of families combinatorial structures which possess a certain regularity. More precisely, we describe how to obtain the differential equations satisfied by their generating series. These…

We define and investigate properties of universal operator algebras of directed graphs. Results include free products decomposition and continuity of the construction with respect to direct limits. Lastly we prove some K-theoretic results…

We provide a general notion of induced structures of operated algebras in the context of unary-binary operads. This notion fully captures the binary quadratic relations encoded by a unary-binary operad, thereby unifying and formalizing the…

Data processing systems roughly group into families such as relational, array, graph, and key-value. Many data processing tasks exceed the capabilities of any one family, require data stored across families, or run faster when partitioned…

For any finite dimensional basic associative algebra, we study the presentation spaces and their relation with the representation spaces. We prove two propositions about a general presentation, one on its subrepresentations and the other on…

The set of prime numbers has been analyzed, based on their algebraic and arithmetical structure. Here by obtaining a sort of linear formula for the set of prime numbers, they are redefined and identified; under a systematic procedure it has…

The goal of this article is to describe several presentations of the infinity category of algebras over some monad on the infinity category of chain complexes.

We characterize when the elementary diagram of a mutually algebraic structure has a model complete theory, and give an explicit description of a set of existential formulas to which every formula is equivalent. This characterization yields…

We give a necessary and sufficient smoothness condition for the scheme parameterizing the n-dimensional representations of a finitely generated associative algebra over an algebraically closed field of characteristic zero. In particular,…

We are going to introduce a new algebraic, analytic structure that is a kind of generalization of the Hausdorff dimension and measure. We give many examples and study the basic properties and relations of such systems.

We study the structure of a family of algebras which encodes a generalization of the Pieri Rule for the complex orthogonal group. In particular, we show that each of these algebras has a standard monomial basis and has a flat deformation to…

Operads were originally defined by May to have right actions of the symmetric groups, but later formulations have also used no groups actions at all or group actions by such families as the braid groups. We call such families action…

We decribe the correspondence between normalised $\omega$-operads and certain lax monoidal structures on the category of globular sets. As with ordinary monoidal categories, one has a notion of category enriched in a lax monoidal category.…

Let $G$ be a complex affine algebraic group, and let $\sigma_1$ and $\sigma_2$ be commuting anti-holomorphic involutions of $G$. We construct an algebraic family of algebraic groups over the complex projective line and a real structure on…

We construct an explicit filtration of the ring of algebraic power series by finite dimensional constructible sets, measuring the complexity of these series. As an application, we give a bound on the dimension of the set of algebraic power…

We argue that operads provide a general framework for dealing with polynomials and combinatory completeness of combinatory algebras, including the classical $\mathbf{SK}$-algebras, linear $\mathbf{BCI}$-algebras, planar…

We study the square of opposition and its various geometric generalizations from an algebraic viewpoint. In particular, we show how the various shapes of oppositions can be framed under an algebraic framework and we illustrate this approach…

We show that the symmetrization of a brace algebra structure yields the structure of a symmetric brace algebra.