Related papers: Opetopic algebras I: Algebraic structures on opeto…
In this note we study a family of algebras with one parameter defined by generators and relations. The set of generators contains the generators of the usual braids algebra, and another set of generators which is interpreted as ties between…
We describe a model structure for coloured operads with values in the category of symmetric spectra (with the positive model structure), in which fibrations and weak equivalences are defined at the level of the underlying collections. This…
This paper studies the existence of model category structures on algebras and modules over operads in monoidal model categories.
Starting from a biased definition of a properad, we describe explicitly algebras over the cobar construction of a properad. Equivalent description in terms of solutions of generalized master equations, which can be interpreted as…
We recall several categories of graphs which are useful for describing homotopy-coherent versions of generalized operads (e.g. cyclic operads, modular operads, properads, and so on), and give new, uniform definitions for their morphisms.…
A class of algebras is constructed using free fermions and the invariant antisymmetric tensors associated with irreducible holonomy groups. (This version contains minor typographical corrections and some additional references. )
Universal algebraic geometry allows considering of geometric properties of every universal algebra. When two algebras have same algebraic geometry? We must consider the categories of algebraic closed sets of these algebras to answer this…
Many statistical models are algebraic in that they are defined in terms of polynomial constraints, or in terms of polynomial or rational parametrizations. The parameter spaces of such models are typically semi-algebraic subsets of the…
Parallel to operated algebras built on top of planar rooted trees via the grafting operator $B^+$, we introduce and study $\vee$-algebras and more generally $\vee_\Omega$-algebras based on planar binary trees. Involving an analogy of the…
We develop a direct method to recover an orthoalgebra from its poset of Boolean subalgebras. For this a new notion of direction is introduced. Directions are also used to characterize in purely order-theoretic terms those posets that are…
After introducing some motivations for this survey, we describe a formalism to parametrize a wide class of algebraic structures occurring naturally in various problems of topology, geometry and mathematical physics. This allows us to define…
We define topological orthoalgebras (TOAs) and study their properties. While every topological orthomodular lattice is a TOA, the lattice of projections of a Hilbert space is an example of a lattice-ordered TOA that is not a toplogical…
We introduce a framework to define coalgebra and bialgebra structures on two-dimensional (2D) square lattices, extending the algebraic theory of Hopf algebras and quantum groups beyond the one-dimensional (1D) setting. Our construction is…
We define Jones's planar algebra as a map of multicategories and constuct a planar algebra starting from a 1-cell in a pivotal strict 2-category. We prove finiteness results for the affine representations of finite depth planar algebras. We…
The notion of the genus of a quadratic form is generalized to vertex operator algebras. We define it as the modular braided tensor category associated to a suitable vertex operator algebra together with the central charge. Statements…
A functor from the category of directed trees with inclusions to the category of commutative C*-algebras with injective *-homomorphisms is constructed. This is used to define a functor from the category of directed graphs with inclusions to…
Orthogonality is a notion based on the duality between programs and their environments used to determine when they can be safely combined. For instance, it is a powerful tool to establish termination properties in classical formal systems.…
There has been a great deal of research on graphs defined on algebraic structures in the last two decades. In this paper we begin an exploration of hypergraphs defined on algebraic structures, especially groups, to investigate whether this…
We introduce unary operadic 2-categories as a framework for operadic Grothendieck construction for categorical $\mathbb{O}$-operads, $\mathbb{O}$ being a unary operadic category. The construction is a fully faithful functor…
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…