Related papers: Linear representations of formal loops
The continuous Moufang loops are characterized as the algebraic systems where the associativity law is perturbed minimally. The minimal perturbation of associativity is characterized by the first- order partial differential equations, which…
We review some recent advances in modular representation theory of symmetric groups and related Hecke algebras. We discuss connections with Khovanov-Lauda-Rouquier algebras and gradings on the blocks of the group algebras $F\Sigma_n$, which…
We show that the (2-)category of categorical representations of the loop group embeds fully faithfully into the (2-)category of factorization module categories with respect to the affine Grassmannian.
Generators and relations are given for the subalgebra of cocommutative elements in the quantized coordinate rings of the classical groups, where the deformation parameter q is transcendental. This is a ring theoretic formulation of the well…
We first motivate the study of a certain quotient of the loop braid category, both for the mathematics underpinning recent approaches to topological quantum computation; and as a key example in non-semisimple higher representation theory.…
A new representation of Quantum Gravity is developed. This formulation is based on an extension of the group of loops. The enlarged group, that we call the Extended Loop Group, behaves locally as an infinite dimensional Lie group. Quantum…
We introduce a class of non-Moufang loops satisfying the Moufang's theorem.
We study the interpolation group whose elements are suitable pairs of formal power series. This group has a faithful representation into infinite lower triangular matrices and carries thus a natural structure as a Lie group. The matrix…
We introduce the notion of (twisted) quiver representations in abelian categories and study the category of such representations. We construct standard resolutions and coresolutions of quiver representations and study basic homological…
We consider a constructive modification of quantum-mechanical formalism. Replacement of a general unitary group by unitary representations of finite groups makes it possible to reproduce quantum formalism without loss of its empirical…
Exact indecomposable module categories over the tensor category of representations of Hopf algebras that are liftings of quantum linear spaces are classified.
We describe an linear representation for Abel-Grassmann groups. As a consequence, we obtain or improve many previous results. In particular, enumeration of Abel-Grassmann groups up to isomorphism is obtained for orders <512.
Let $V$ be a cubic surface defined by the equation $T_0^3+T_1^3+T_2^3+\theta T_3^3=0$ over a quadratic extension of 3-adic numbers $k=\mathbb{Q}_3(\theta)$, where $\theta^3=1$. We show that a relation on a set of geometric k-points on $V$…
Periodic table of chemical elements symbolizes an elegant graphical representation of symmetry at atomic level and provides an overview on arrangement of electrons. It started merely as tabular representation of chemical elements, later got…
The category of admissible (in the appropriately modified sense of representation theory of totally disconnected groups) semi-linear representations of the automorphism group of an algebraically closed extension of infinite transcendence…
It is shown that the groups of Euclidian rotations, rigid motions, proper, orthochronous Lorentz transformations, and the complex rigid motions can be represented by the groups of unit-norm elements in the algebras of real, dual, complex,…
A set of coordinates in the non parametric loop-space is introduced. We show that these coordinates transform under infinite dimensional linear representations of the diffeomorphism group. An extension of the group of loops in terms of…
The linear representation hypothesis is the informal idea that semantic concepts are encoded as linear directions in the representation spaces of large language models (LLMs). Previous work has shown how to make this notion precise for…
The rings of symmetric polynomials form an inverse system whose limit, the ring of symmetric functions, is the model for the bosonic Fock space representation of the affine Lie algebra. We categorify this construction by considering an…
This paper defines a linear representation for nonlinear maps $F:\mathbb{F}^n\rightarrow\mathbb{F}^n$ where $\mathbb{F}$ is a finite field, in terms of matrices over $\mathbb{F}$. This linear representation of the map $F$ associates a…