Related papers: Embeddings of representations
We study atom canonicity for several varieties of cylindric like algebras that contain properly the variety of representable algebras. The algebras in such varieties have relativized representations, and we thereby obtain many omitting…
We establish a number of results which say, roughly, that interpretation functors preserve algebraic complexity. First we show that representation embeddings between categories of modules of finite-dimensional algebras induce embeddings of…
Symmetries and reductions of some algebraic equations are considered. Transformations that preserve the form of several algebraic equations, as well as transformations that reduce the degree of these equations, are described. Illustrative…
We show that atomic polyadic algebras of infinite dimensions are completely representable
We classify the finite dimensional irreducible representations of rectangular finite $W$-algebras, i.e., the finite $W$-algebras $U(\mathfrak{g}, e)$ where $\mathfrak{g}$ is a symplectic or orthogonal Lie algebra and $e \in \mathfrak{g}$ is…
The form factors of integrable models in finite volume are studied. We construct the explicite representations for the form factors in terms of determinants.
We classify irreducible unitary representations of the group of all infinite matrices over a $p$-adic field ($p\ne 2$) with integer elements equipped with a natural topology. Any irreducible representation passes through a group $GL$ of…
We present alternative postulates for Euclidean geometry whose merit is that they lead to a new class of invariants and associated geometries for real finite-dimensional unital associative algebras.
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…
This paper introduces the notion of calibrated representations for affine Hecke algebras and classifies and constructs all finite dimensional irreducible calibrated representations. The main results are that (1) irreducible calibrated…
Using the algebraic classification of all $2$-dimensional algebras, we give the algebraic classification of all $2$-dimensional rigid, conservative and terminal algebras over an algebraically closed field of characteristic 0. We have the…
We present integral representations of solutions to division problems involving matrices of polynomials in several complex variables. We also find estimates of the polynomial degree of the solutions by means of careful degree estimates of…
Quantitative bounds for random embeddings of $\mathbb{R}^{k}$ into Lorentz sequence spaces are given, with improved dependence on $\varepsilon$.
We define reflective numbers and their iterative summations. We provide classification of reflective numbers based on their iterative cyclical limits.
We prove that every finite dimensional representation of a finite group over a field of characteristic p admits a finite resolution by p-permutation modules. The proof involves a reformulation in terms of derived categories.
To every finite-dimensional $\mathbb C$-algebra $\Lambda$ of finite representation type we associate an affine variety. These varieties are a large generalization of the varieties defined by "$u$ variables" satisfying "$u$-equations", first…
The study of graph drawings on 2-surfaces is an active area of mathematical research. Our main results are criteria for integer and modulo 2 embeddability of graphs to surfaces.
A set A of natural numbers is finitely embeddable in another such set B if every finite subset of A has a rightward translate that is a subset of B. This notion of finite embeddability arose in combinatorial number theory, but in this paper…
We introduce a novel embedding method diverging from conventional approaches by operating within function spaces of finite dimension rather than finite vector space, thus departing significantly from standard knowledge graph embedding…
We characterize unitary representations of braid groups $B_n$ of degree linear in $n$ and finite images of such representations of degree exponential in $n$.