Related papers: The higher relation bimodule

We define global and local Weyl modules for $q \otimes A$, where $q$ is the queer Lie superalgebra and $A$ is an associative commutative unital $\mathbb{C}-$algebra. We prove that global Weyl modules are universal highest weight objects in…

In this note we extend the spectral theorem for bimodules to the higher rank graph C*-algebra context. Under the assumption that the graph is row finite and has no sources, we show that a bimodule over a natural abelian subalgebra is…

In this paper we construct a large class of modules for toroidal Lie superalgebras. Toroidal Lie superalgebras are universal central extension of G tensor A where G is a basic classical Lie superalgebra and A is a Laurent polynomial ring in…

We study generic objects in triangulated categories and characterize the finite dimensional algebras $A$ such that the derived categories $D(\Mod A)$ are generically trivial. This is an analogue of a result of Crawley-Boevey for module…

We classify, up to derived (equivalently, tilting-cotilting) equivalence all nondegenerate gentle two-cycle algebras. We also give a partial classification and formulate a conjecture in the degenerate case.

We present methods and explicit formulas for describing simple weight modules over twisted generalized Weyl algebras. When a certain commutative subalgebra is finitely generated over an algebraically closed field we obtain a classification…

It is proved that uniformly bounded simple modules over higher rank super-Virasoro algebras are modules of the intermediate series, and that simple modules with finite dimensional weight spaces are either modules of the intermediate series…

We study the Ext modules in the category of left modules over a twisted algebra of a finite quiver over a ringed space $(X,\mathcal O_X)$, allowing for the presence of relations. We introduce a spectral sequence which relates the Ext…

An algebra extension A | B is right depth two if its tensor-square A\otimes_B A is in the Dress category Add A as A-B-bimodules. We consider necessary conditions for right, similarly left, D2 extensions in terms of partial A-invariance of…

In this note we are concerned with the notion of amenable representation type as defined in a recent paper by G\'abor Elek. Roughly speaking, an algebra is of amenable type if for all $\varepsilon > 0$, every finite-dimensional module has a…

For each valued quiver $Q$ of Dynkin type, we construct a valued ice quiver $\Delta_Q^2$. Let $G$ be a simple connected Lie group with Dynkin diagram the underlying valued graph of $Q$. The upper cluster algebra of $\Delta_Q^2$ is graded by…

We show that string algebras are `homologically tame' in the following sense: First, the syzygies of arbitrary representations of a finite dimensional string algebra $\Lambda$ are direct sums of cyclic representations, and the left…

Let $\mathfrak g$ be a complex simple Lie algebra and let $\Psi$ be an extremal set of positive roots. One associates with $\Psi$ an infinite dimensional Koszul algebra $\bold S_\Psi^{\lie g}$ which is a graded subalgebra of the locally…

In this article, we study Dorroh extensions of algebras and Dorroh extensions of coalgebras. Their structures are described. Some properties of these extensions are presented. We also introduce the finite duals of algebras and modules which…

This paper studies the twisted representations of vertex operator algebras. Let V be a vertex operator algebra and g an automorphism of V of finite order T. For any m,n in (1/T)Z_+, an A_{g,n}(V)-A_{g,m}(V)-bimodule A_{g,n,m}(V) is…

We prove that a finite von Neumann algebra ${\mathcal A}$ is semisimple if the algebra of affiliated operators ${\mathcal U}$ of ${\mathcal A}$ is semisimple. When ${\mathcal A}$ is not semisimple, we give the upper and lower bounds for the…

Let $G$ be a connected reductive algebraic group over a field of positive characteristic $p$ and denote by $\mathcal T$ the category of tilting modules for $G$. The higher Jones algebras are the endomorphism algebras of objects in the…

It is proved that a multiset of permissible arcs over a tiling is uniquely determined by its intersection vector under a mild condition. This generalizes a classical result over marked surfaces with triangulations. We apply this result to…

It is shown that certain transformations on quiver-dimension vector pairs induce isomorphisms on the corresponding moduli spaces of quiver representations and map a stable dimension vector to a stable dimension vector. This result combined…

Let H be a finite-dimensional Hopf algebra. We give a description of the tensor product of bimodule categories over Rep(H). When the bimodule categories are invertible this description can be given explicitly. We present some consequences…