Related papers: Generic representation theory of quivers with rela…
In this paper we study the representation theory for certain ``half lattice vertex algebras.'' In particular we construct a large class of irreducible modules for these vertex algebras. We also discuss how the representation theory of these…
Let $\mathbf{k}$ be an algebraically closed field, let $\Lambda$ be a finite dimensional $\mathbf{k}$-algebra, and let $\widehat{\Lambda}$ be the repetitive algebra of $\Lambda$. For the stable category of finitely generated left…
Let $Q$ be a finite quiver without oriented cycles and $k$ an algebraically closed field.In this paper we establish a connection between cluster algebras and the representation theory of the path algebra $kQ$, in terms of the spectral…
We provide a unified approach, via deformations of incidence algebras, to several important types of representations with finiteness conditions, as well as the combinatorial algebras which produce them. We show that over finite dimensional…
We study cyclic adjoint modules arising from the relative locally finite part of the adjoint action of a quantum Levi subalgebra on a quantized enveloping algebra. We classify embeddings of finite-dimensional irreducible modules inside of…
We introduce unbounded strongly irreducible operators and transitive operators. These operators are related to a certain class of indecomposable Hilbert representations of quivers on infinite-dimensional Hilbert spaces. We regard the theory…
Let n be a positive integer, and let R be a finitely presented (but not necessarily finite dimensional) associative algebra over a computable field. We examine algorithmic tests for deciding (1) if every n-dimensional representation of R is…
The Weil representation of the symplectic group associated to a finite abelian group of odd order is shown to have a multiplicity-free decomposition. When the abelian group is p-primary, the irreducible representations occurring in the Weil…
In this article, we study the representation theory of shifted super Yangians and finite $W$-superalgebras of type A. A criterion for the finite dimensionality of irreducible modules is obtained in the standard parity case. Furthermore, we…
We study the modular representation theory of the symmetric and alternating groups. One of the most natural ways to label the irreducible representations of a given group or algebra in the modular case is to show the unitriangularity of the…
Quivers play an important role in the representation theory of algebras, with a key ingredient being the path algebra and the preprojective algebra. Quiver grassmannians are varieties of submodules of a fixed module of the path or…
In this paper we show that the fields of rational invariants over the irreducible components of the module varieties for an acyclic gentle algebra are purely transcendental extensions. Along the way, we exhibit for such fields of rational…
The underlying algebra for a noncommutative geometry is taken to be a matrix algebra, and the set of derivatives the adjoint of a subset of traceless matrices. This is sufficient to calculate the dual 1-forms, and show that the space of…
We initiate the systematic study of endomorphism algebras of permutation modules and show they are obtainable by a descent from a certain "generic" Hecke algebra, infinite-dimensional in general, coming from the universal enveloping algebra…
Suppose $g=g_0+g_1$ is a finite-dimensional restricted Lie superalgebra over an algebraically closed field $k$ of characteristic $p>2$. In this article, we propose a conjecture for maximal dimensions of irreducible modules over the…
For a zero-relation algebra over a field $\mathcal K$, Crawley-Boevey introduced the concept of a tree module and provided a combinatorial description of a basis for the space of homomorphisms between two tree modules--the basis elements…
We completely characterize perfect, permutative, irreducible representations of an ultragraph Leavitt path algebra. For this we extend to ultragraph Leavitt path algebras Chen's construction of irreducible representations of Leavitt path…
We study a family of three-dimensional Lie algebras $L_\mu$ that depend on a continuous parameter $\mu$. We introduce certain quivers, which we denote by $Q_{m,n}$ $(m,n \in \mathbb{Z})$ and $Q_{\infty \times \infty}$, and prove that…
From the viewpoint of higher dimensional Auslander-Reiten theory, we introduce a new class of finite dimensional algebras of global dimension n, which we call n-representation infinite. They are a certain analog of representation infinite…
We investigate the representations of the exotic conformal Galilei algebra. This is done by explicitly constructing all singular vectors within the Verma modules, and then deducing irreducibility of the associated highest weight quotient…