相关论文: A Brauerian Representation of Split Preorders
The Rankin--Cohen brackets provide a basic example of ``non-elementary" differential symmetry breaking operators. They can be interpreted as bi-differential operators remarkable for reflecting the structure of fusion rules for holomorphic…
A number of recent papers treated the representation theory of partially ordered sets in unitary spaces with the so called orthoscalar relation. Such theory generalizes the classical theory which studies the representations of partially…
The main object of study of this paper is the notion of a LieDer pair, i.e. a Lie algebra with a derivation. We introduce the concept of a representation of a LieDer pair and study the corresponding cohomologies. We show that a LieDer pair…
We introduce the calculus of neo-Peircean relations, a string diagrammatic extension of the calculus of binary relations that has the same expressivity as first order logic and comes with a complete axiomatisation. The axioms are obtained…
A folklore result in category theory is that a (weakly) Cartesian closed category with finite co-products is distributive. Usually, the proof of this small result is carried on using the fact that the exponential functor is right adjoint to…
There are two kinds of splittings of operations, namely, the classical splitting which is interpreted operadically as taking successors and another splitting which we call the second splitting giving the anti-structures of the successors'…
The first part of this thesis studies the notion of a "quantum representation", introduced by J.-M. Souriau in order to provide a polarization-free characterization of the Lie group representations attached to coadjoint orbits. When the…
In this article, we compare the cohomology between the categories of modules of the diagram algebras and the categories of modules of its input algebras. Our main result establishes a sufficient condition for exact split pairs between these…
We exhibit an adjunction between a category of abstract algebras of partial functions and a category of set quotients. The algebras are those atomic algebras representable as a collection of partial functions closed under relative…
In this paper we study the notion of first-order part of a computational problem, first introduced by Dzhafarov, Solomon, and Yokoyama, which captures the "strongest computational problem with codomain $\mathbb{N}$ that is Weihrauch…
Definite descriptions are first-order expressions that denote unique objects. In this paper, we propose a second-order counterpart, designed to refer to unique relations between objects. We investigate this notion within the framework of…
The notion of pre-Leibniz algebras was recently introduced in the study of Rota-Baxter operators on Leibniz algebras. In this paper, we first construct a graded Lie algebra whose Maurer-Cartan elements are pre-Leibniz algebras. Using this…
We study the relative complexity of equivalence relations and preorders from computability theory and complexity theory. Given binary relations $R, S$, a componentwise reducibility is defined by $ R\le S \iff \ex f \, \forall x, y \, [xRy…
Classical planning representation languages based on first-order logic have preliminarily been used to model and solve robotic task planning problems. Wider adoption of these representation languages, however, is hindered by the limitations…
This paper presents the first in a series of results that allow us to develop a theory providing finer control over the complexity of normalisation, and in particular of cut elimination. By considering atoms as self-dual non-commutative…
We show that a divisor in a rational homogenous variety with split normal sequence is the preimage of a hyperplane section in either the projective space or a quadric.
We study the categorical properties of right-preordered groups, giving an explicit description of limits and colimits in this category, and studying some exactness properties. We show that, from an algebraic point of view, the category of…
We show that in the category of preordered sets, there is a natural notion of pretorsion theory, in which the partially ordered sets are the torsion-free objects and the sets endowed with an equivalence relation are the torsion objects.…
We introduce the oriented Brauer-Clifford and degenerate affine oriented Brauer-Clifford supercategories. These are diagrammatically defined monoidal supercategories which provide combinatorial models for certain natural monoidal…
We show that bounded type implies finite type for a constructible subcategory of the module category of a finitely generated algebra over a field, which is a variant of the first Brauer-Thrall conjecture. A full subcategory is constructible…