相关论文: Identities for mixed representations of quiver are…
We consider $m$-cluster tilted algebras arising from quivers of Euclidean type and we give necessary and sufficient conditions for those algebras to be representation finite. For the case $\widetilde{A}$, using the geometric realization, we…
We use representation theory to construct spaces of matrices of constant rank. These spaces are parametrized by the natural representation of the general linear group or the symplectic group. We present variants of this idea, with more…
Let R be the connected component of the identity of the variety of representations of a finitely generated nilpotent group N into a connected reductive complex affine algebraic group G. We determine the mixed Hodge structure on the…
Bilinear maps and their classifying tensor products are well-known in the theory of linear algebra, and their generalization to algebras of commutative monads is a classical result of monad theory. Motivated by constructions needed in…
An algebraic investigation on bicomplex numbers is carried out here. Particularly matrices and linear maps defined on them are discussed. A new kind of cartesian product, referred to as an idempotent product, is introduced and studied. The…
We derive "numerical" criteria for the existence of embeddings of representations of finite dimensional algebras.
Generative concept representations have three major advantages over discriminative ones: they can represent uncertainty, they support integration of learning and reasoning, and they are good for unsupervised and semi-supervised learning. We…
We exhibit a set of generating relations for the modular invariant ring of a vector and a covector for the two-dimensional general linear group over a finite field.
We characterize the indecomposable injective objects in the category of finitely presented representations of an interval finite quiver.
The K-partitioning problem consists of partitioning the vertices of a graph in K sets so as to minimize a function of the edge weights. We introduce a linear mixed integer formulation with edge variables and representative variables. We…
We study indecomposable representations of quivers on separable infinite-dimensional Hilbert spaces by bounded operators. We consider a complement of Gabriel's theorem for these representations. Let $\Gamma$ be a finite, connected quiver.…
We consider an arbitrary representation of the additive group over a field of characteristic zero and give an explicit description of a finite separating set in the corresponding ring of invariants.
This article discusses the geometric application of the method of multiplier ideal sheaves. It first briefly describes its application to effective problems in algebraic geometry and then presents and explains its application to the…
In this paper we give a simple description of DT-invariants of double quivers without potential as the multiplicity of the Steinberg character in some representation associated with the quiver. When the dimension vector is indivisible we…
We give a simplified complete proof for the classification of the selfinjective representation-finite algebras of finite dimension over an algebraically closed field. We explain the relations between the two different approaches and also to…
The connections amongst (1) quivers whose representation varieties are Calabi-Yau, (2) the combinatorics of bipartite graphs on Riemann surfaces, and (3) the geometry of mirror symmetry have engendered a rich subject at whose heart is the…
In this paper we construct strong exceptional collections of vector bundles on smooth projective varieties that have a prescribed endomorphism algebra. We prove the construction problem always have a solution. We consider some applications…
The irreducible components of varieties parametrizing the finite dimensional representations of a finite dimensional algebra $\Lambda$ are explored, with regard to both their geometry and the structure of the modules they encode. Provided…
We consider the dimensions of finite type of representations of a partially ordered set, i.e. such that there is only finitely many isomorphism classes of representations of this dimension. We give a criterion for a dimension to be of…
We initiate a study of infinite tensor products of projective unitary representations of a discrete group G. Special attention is given to regular representations twisted by 2-cocycles and to projective representations associated with…