Related papers: On the classification of graded twisted planes
In this paper, we introduce a class of twisted matrix algebras of $M_2(E)$ and twisted direct products of $E\times E$ for an algebra $E$. Let $A$ be a noetherian Koszul Artin-Schelter regular algebra, $z\in A_2$ be a regular central element…
We give analogues of the Auslander correspondence for two classes of triangulated categories satisfying certain finiteness conditions. The first class is triangulated categories with additive generators and we consider their endomorphism…
We introduce what we call "alternative twisted tensor products" for not necessarily associative algebras, as a common generalization of several different constructions: the Cayley-Dickson process, the Clifford process and the twisted tensor…
We introduce a new class of algebras, which we call cluster-tilted. They are by definition the endomorphism algebras of tilting objects in a cluster category. We show that their representation theory is very close to the representation…
In this paper we introduce a new and large family of configurations whose toric ideals possess quadratic Groebner bases. As an application, a generalization of algebras of Segre-Veronese type will be studied.
We construct a categorification of the modular data associated with every family of unipotent characters of the spetsial complex reflection group $G(d,1,n)$. The construction of the category follows the decomposition of the Fourier matrix…
Tensor type data are becoming important recently in various application fields. We determine a rank of a tensor T so that A+T is diagonalizable for a given 3-tensor A with 2 slices over the complex and real number field.
We introduce a new class of graded rings extending the class of generalized Weyl algebras. These rings are orders in crossed products of the most general type, and we introduce their basic structure theory. We provide an extensive list of…
Given a vector bundle $A\to M$ we study the geometry of the graded manifolds $T^*[k]A[1]$, including their canonical symplectic structures, compatible Q-structures and Lagrangian Q-submanifolds. We relate these graded objects to classical…
We generalise Koszul and D-Koszul algebras by introducing a class of graded algebras called (D,A)-stacked algebras. We give a characterisation of (D,A)-stacked algebras and show that their Ext algebra is finitely generated as an algebra in…
In this paper, we complete the classification of representation-finite tensor product algebras in terms of quiver with relations.
We introduce an infinite family of Kronecker series twisted by characters. As an application, we give a closed formula for the sum of all Hecke eigenforms on ${\Gamma}_0(N) $ multiplied by their twisted period polynomials in terms of the…
It is known that the notion of graded differential algebra coincides with the notion of monoid in the monoidal category of complexes. By using the monoidal structure introduced by M. Kapranov for the category of $N$-complexes we define the…
We give an explicit description of the mutation classes of quivers of type \tilde{A}_n. Furthermore, we provide a complete classification of cluster tilted algebras of type \tilde{A}_n up to derived equivalence. We show that the bounded…
This article surveys results on graded algebras and their Hilbert series. We give simple constructions of finitely generated graded associative algebras $R$ with Hilbert series $H(R,t)$ very close to an arbitrary power series $a(t)$ with…
We define united K-theory for real C*-algebras, generalizing Bousfield's topological united K-theory. United K-theory incorporates three functors -- real K-theory, complex K-theory, and self-conjugate K-theory -- and the natural…
The usual crossed product construction which associates to the homeomorphism $T$ of the locally compact space $X$ the C$^*$-algebra $C^*(X,T)$ is extended to the case of a partial local homeomorphism $T$. For example, the Cuntz-Krieger…
If $A$ and $B$ are $n$- and $m$-representation finite $k$-algebras, then their tensor product $\Lambda = A\otimes_k B$ is not in general $(n+m)$-representation finite. However, we prove that if $A$ and $B$ are acyclic and satisfy the weaker…
In this paper, twisted tensor product of DG algebras is studied and sufficient conditions for smoothness of such a product are given. It is shown that in the case of finite-dimensional DG algebras, applying this operation offers great…
We introduce two classes of algebras coming from partial triangulations of marked surfaces. The first one, called frozen algebra of a partial triangulation, is generally of infinite rank and contains frozen Jacobian algebras of…