Related papers: Representation Embeddings of Cartesian Theories
The Topological Representation Theorem for (oriented) matroids states that every (oriented) matroid can be realized as the intersection lattice of an arrangement of codimension one homotopy spheres on a homotopy sphere. In this paper, we…
The irreducible components of varieties parametrizing the finite dimensional representations of a finite dimensional algebra $\Lambda$ are explored, with regard to both their geometry and the structure of the modules they encode. Provided…
This book is mainly an exposition of the author's works and his joint works with his former students on explicit representations of finite-dimensional simple Lie algebras, related partial differential equations, linear orthogonal algebraic…
We show that for any finite-dimensional algebra $\Lambda$ of infinite representation type, over a perfect field, there is a bounded principal ideal domain $\Gamma$ and a representation embedding from $\Gamma -$mod into $\Lambda -$mod. As an…
We develop the representation theory of a finite semigroup over an arbitrary commutative semiring with unit, in particular classifying the irreducible and minimal representations. The results for an arbitrary semiring are as good as the…
We study the degree of irreducible morphisms in any Auslander-Reiten component of a finite dimensional algebra over an algebraically closed field. We give a characterization for an irreducible morphism to have finite left (or right) degree.…
We give a survey on the theory of representation-finite and certain minimal representation-infinite algebras.The main goals are the existence of multiplicative bases and of coverings with good properties. Both are attained via…
We prove that the problems of representing a finite ordered complemented semigroup or finite lattice-ordered semigroup as an algebra of binary relations over a finite set are undecidable. In the case that complementation is taken with…
We say that there is a representation of the universal algebra B in the universal algebra A if the set of endomorphisms of the universal algebra A has the structure of universal algebra B. Therefore, the role of representation of the…
Lurie's representability theorem gives necessary and sufficient conditions for a functor to be an almost finitely presented derived geometric stack. We establish several variants of Lurie's theorem, making the hypotheses easier to verify…
A representation theorem for non-semibounded Hermitian quadratic forms in terms of a (non-semibounded) self-adjoint operator is proven. The main assumptions are closability of the Hermitian quadratic form, the direct integral structure of…
This thesis concerns embeddings and self-embeddings of foundational structures in both set theory and category theory. The first part of the work on models of set theory consists in establishing a refined version of Friedman's theorem on…
A model of representations of a Lie algebra is a representation which a direct sum of all irreducible finite dimensional representations taken with multiplicity $1$. In the paper an explicit construction of a model of representation for all…
A central question in cognitive science is whether conceptual representations converge onto a shared manifold to support generalization, or diverge into orthogonal subspaces to minimize task interference. While prior work has discovered…
We introduce a strategy to study irreducible representations of automorphism groups of finite modules over local rings. We prove that these automorphism groups fit in a hierarchy that facilitates a stratification of their irreducible…
We classify globally irreducible representations of alternating groups and double covers of symmetric and alternating groups. In order to achieve this classification we also completely characterise irreducible representations of such groups…
Knowledge graph embedding has recently become a popular way to model relations and infer missing links. In this paper, we present a group theoretical perspective of knowledge graph embedding, connecting previous methods with different group…
Compositionality is a key aspect of human intelligence, essential for reasoning and generalization. While transformer-based models have become the de facto standard for many language modeling tasks, little is known about how they represent…
Suppose a finite group acts on a scheme X and a finite-dimensional Lie algebra g. The corresponding equivariant map algebra is the Lie algebra M of equivariant regular maps from X to g. We classify the irreducible finite-dimensional…
In this paper, we describe the irreducible representations and give a dimension formula for the Framisation of the Temperley-Lieb algebra. We then prove that the Framisation of the Temperley-Lieb algebra is isomorphic to a direct sum of…