Related papers: Multilinear representations of Free PROs
We study modular ortholattices in the variety generated by the finite dimensional ones from an equational and geometric point of view. We relate this to coordinatization results.
The exact parameter values of mathematical models are often uncertain or even unknown. Nevertheless, we may have access to crude information about the parameters, e.g., that some of them are nonzero. Such information can be captured by…
Every real hyperbolic form in three variables can be realized as the determinant of a linear net of Hermitian matrices containing a positive definite matrix. Such representations are an algebraic certificate for the hyperbolicity of the…
In this paper polynomial maps are represented by the use of matrices whose entries are numbered by pair of multiindices and a new product of such matrices is introduced. A matrix representation of composition of polynomial maps is given. In…
We characterize when the level sets of a continuous quasi-monotone functional defined on a suitable convex subset of a normed space can be uniquely represented by a family of bounded continuous functionals. Furthermore, we investigate how…
In this paper, we introduce a representation theory of Hom-Lie conformal superalgebras and discuss the cases of adjoint representations. Furthermore, we develop cohomology theory of Hom-Lie conformal superalgebras and discuss some…
In this exposition, we get examples of what is called a "linear hyperdoctrine", based on categories of comodules indexed by coalgebras. This structures can model first order linear logic.
In this paper we discuss representations of the Birman-Wenzl-Murakami algebra as well as of its dilute extension containing several free parameters. These representations are based on superalgebras and their baxterizations permit us to…
Parametric entities appear in many contexts, be it in optimisation, control, modelling of random quantities, or uncertainty quantification. These are all fields where reduced order models (ROMs) have a place to alleviate the computational…
This note contributes to the structure theory of abstract rigidity matroids in general dimension. In the spirit of classical matroid theory, we prove several cryptomorphic characterizations of abstract rigidity matroids (in terms of…
We introduce a deep multitask architecture to integrate multityped representations of multimodal objects. This multitype exposition is less abstract than the multimodal characterization, but more machine-friendly, and thus is more precise…
In this paper we discuss various philosophical aspects of the hyperstructure concept extending networks and higher categories. By this discussion we hope to pave the way for applications and further developments of the mathematical theory…
We construct free-field resolutions of unitary representations of the N=2 superconformal algebra. The irreducible representations are singled out from free-field spaces as the cohomology of fermionic screening operators. We construct and…
In this paper we explore the representation property over sets. This property generalizes constructibility, however is weak enough to enable us to prove that the class of theories $T$ whose models are representable is exactly the class of…
A new approach to massive integrable models is considered. It allows one to find symmetry algebras which define spaces of local operators and to get general integral representations for form-factors in the\ $ SU(2)$\ Thirring and…
We clarify the linear algebra used in the quaternionic pluripotential theory so that proofs of several results there can be greatly simplified. In particular, we characterize and normalize real $2$-forms with respect to the quaternionic…
We study probability distributions over free algebras of trees. Probability distributions can be seen as particular (formal power) tree series [Berstel et al 82, Esik et al 03], i.e. mappings from trees to a semiring K . A widely studied…
The structure of representations describing systems of free particles in the theory with the invariance group SO(1,4) is investigated. The property of the particles to be free means as usual that the representation describing a…
In this paper we first state the classification of the prolongations of complex free fundamental graded Lie algebras. Next we introduce the notion of free pseudo-product fundamental graded Lie algebras and study the prolongations of complex…
Motivated by its link with functor homology, we study the prop freely generated by the operadic suspension of the operad Com. We exhibit a particular family of generators, for which the composition and the symmetric group actions admit…