Related papers: Representability in Supergeometry
We construct Grothendieck topologies on the path category of a finite graph, examining both coarse and discrete cases that offer different perspectives on quiver representations. The coarse topology declares each vertex covered by all…
Convergence spaces are a generalization of topological spaces. The category of convergence spaces is well-suited for Algebraic Topology, one of the reasons is the existence of exponential objects provided by continuous convergence. In this…
We provide numerical evidence demonstrating the necessity of employing a superparametric geometry representation in order to obtain optimal convergence orders on two-dimensional domains with curved boundaries when solving the Euler…
This paper lays out a foundation for a theory of supertropical algebraic geometry, relying on commutative $\nu$-algebra. To this end, the paper introduces $\mathfrak{q}$-congruences, carried over $\nu$-semirings, whose distinguished ghost…
Theory of representations of universal algebra is a natural development of the theory of universal algebra. In the book, I considered representation of universal algebra, diagram of representations and examples of representation. Morphism…
Many interesting classes of maps from homotopical algebra can be characterised as those maps with the right lifting property against certain sets of maps (such classes are sometimes referred to as cofibrantly generated). In a more…
Representation learning on graphs is a fundamental problem that can be crucial in various tasks. Graph neural networks, the dominant approach for graph representation learning, are limited in their representation power. Therefore, it can be…
We describe explicitly the Grothendieck rings of finite-dimensional representations of the periplectic Lie superalgebras. In particular, the Grothendieck ring of the Lie supergroup $P(n)$ is isomorphic to the ring of symmetric polynomials…
We reformulate superalgebra and supergeometry in completely categorical terms by a consequent use of the functor of points. The increased abstraction of this approach is rewarded by a number of great advantages. First, we show that one can…
We discuss the problem of characterizing the property of a Grothendieck topos to satisfy a given 'geometric' invariant as a property of its sites of definition, and indicate a set of general techniques for establishing such criteria. We…
We propose a generalisation of the Jacquet-Langlands correspondence to the whole Grothendieck group of finite lenght admissible representations. As an application we prove some particular cases of the global Jacquet-Langlands…
Numerous Lie supergroups do not admit superunitary representations except the trivial one, e.g., Heisenberg and orthosymplectic supergroups in mixed signature. To avoid this situation, we introduce in this paper a broader definition of…
Covering theory is an important tool in representation theory of algebras, however, the results and the proofs are scattered in the literature. We give an introduction to covering theory at a level as elementary as possible.
Polygon representation learning is essential for diverse applications, encompassing tasks such as shape coding, building pattern classification, and geographic question answering. While recent years have seen considerable advancements in…
In this paper, we study the relation between the cocenter and the representation theory of affine Hecke algebras. The approach is based on the interaction between the rigid cocenter, an important subspace of the cocenter, and the dual…
Toen has interpreted the schematization problem as originally imagined by Grothendieck in "Pursuing Stacks" in such a way that solution(s) to this problem could be given. As he pointed out, there are many solutions available, and he gave…
Theory of representations of F-algebra is a natural development of the theory of F-algebra. Exploring of morphisms of the representation leads to the concepts of generating set and basis of representation. In the book I considered the…
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…
The probability representation, in which cosmological quantum states are described by a standard positive probability distribution, is constructed for minisuperspace models selected by Noether symmetries. In such a case, the tomographic…
We introduce a simple autoencoder based on hyperbolic geometry for solving standard collaborative filtering problem. In contrast to many modern deep learning techniques, we build our solution using only a single hidden layer. Remarkably,…