Related papers: Low dimensional matrix representations for noncomm…
We study the structure and representations of a family of vertex algebras obtained from affine superalgebras by quantum reduction. As an application, we obtain in a unified way free field realizations and determinant formulas for all…
We apply the local removable singularity theorem for minimal laminations and the local picture theorem on the scale of topology to obtain two descriptive results for certain possibly singular minimal laminations of $\mathbb{R}^3$. These two…
We consider selfinjective Artin algebras whose cohomology groups are finitely generated over a central ring of cohomology operators. For such an algebra, we show that the representation dimension is strictly greater than the maximal…
A complete classification and character formulas for finite-dimensional irreducible representations of the rational Cherednik algebra of type A is given. Less complete results for other types are obtained. Links to the geometry of affine…
The objective of this paper is to determine the finite dimensional, indecomposable representations of the algebra that is generated by two complex structures over the real numbers. Since the generators satisfy relations that are similar to…
We study representations of a Leavitt path algebra $L$ of a finitely separated digraph $\Gamma$ over a field. We show that the category of $L$-modules is equivalent to a full subcategory of quiver representations. When $\Gamma$ is a…
It is conjectured that there exist finitely many isomorphism classes of simple endomorphism algebras of abelian varieties of GL_2-type over \Q of bounded dimension. We explore this conjecture when particularized to quaternion endomorphism…
We prove that over an algebraically closed field there is a representation embedding from the category of classical Kronecker-modules without the simple injective into the category of finite-dimensional modules over any…
The observational characteristics of a linear structural equation model can be effectively described by polynomial constraints on the observed covariance matrix. However, these polynomials can be exponentially large, making them impractical…
We prove a general result on presentations of finitely-generated algebras and apply it to obtain nice presentations for some noncommutative algebras arising in the matrix bispectral problem. By "nice presentation" we mean a presentation…
A non associative, noncommutative algebra is defined that may be interpreted as a set of vector modules over a noncommutative surface of rotation. Two of these vector modules are identified with the analogues of the tangent and cotangent…
We discuss the homological algebra of representation theory of finite dimensional algebras and finite groups. We present various methods for the construction and the study of equivalences of derived categories: local group theory, geometry…
We study non-selfadjoint operator algebras that can be entirely understood via their finite-dimensional representations. In contrast with the elementary matricial description of finite-dimensional $\mathrm{C}^*$-algebras, in the…
A brief proof of Lie's classification of finite dimensional subalgebras of vector fields on the complex plane that have a proper Levi decomposition is given. The proof uses basic representation theory of sl(2, C). This, combined with…
The polynomial deformations of the Witten extensions of the U(su(2)) and U(osp(1,2)) algebras are three generator algebras with normal ordering, admitting a two generator subalgebra. The modules and the representations of these algebras are…
Consider a finite-dimensional algebra $A$ and any of its moduli spaces $\mathcal{M}(A,\mathbf{d})^{ss}_{\theta}$ of representations. We prove a decomposition theorem which relates any irreducible component of…
We continue the study of low dimensional linear representations of mapping class groups of surfaces initiated by Franks--Handel and Korkmaz. We consider $(2g+1)$-dimensional complex linear representations of the pure mapping class groups of…
We study intersection theory for differential algebraic varieties. Particularly, we study families of differential hypersurface sections of arbitrary affine differential algebraic varieties over a differential field. We prove the…
We provide a visual and intuitive introduction to effectively calculating in 2-groups along with explicit examples coming from non-abelian 1- and 2-form gauge theory. In particular, we utilize string diagrams, tools similar to tensor…
Using a new definition of rank for representations of semisimple groups sharp results are proved for the decay of matrix coefficients of unitary representations of two types of non-split $p$-adic simple algebraic groups of exceptional type.…