Related papers: Projective resolution of modules over the noncommu…
We develop a Gr\"obner basis theory for a class of algebras that generalizes both PBW-algebras and rings of differential algebras on smooth varieties. Emphasis lies on methods to compute filtrations and graded structures defined by weight…
In earlier work, the author classified rigid representations of a quiver by finitely generated free modules over a principal ideal ring. Here we extend the results to representations of a quiver by finitely generated projective modules over…
We establish a noncommutative generalisation of the Borel-Weil theorem for the Heckenberger-Kolb calculi of the quantum Grassmannians. The result is formulated in the framework of quantum principal bundles and noncommutative complex…
We study non-commutative projective lines over not necessarily algebraic bimodules. In particular, we give a complete description of their categories of coherent sheaves and show they are derived equivalent to certain bimodule species. This…
In the spirit of noncommutative geometry we construct all inequivalent vector bundles over the $(2,2)$-dimensional supersphere $S^{2,2}$ by means of global projectors $p$ via equivariant maps. Each projector determines the projective module…
This paper presents some algorithmic techniques to compute explicitly the noetherian operators associated to a class of ideals and modules over a polynomial ring. The procedures we include in this work can be easily encoded in computer…
We give a construction of Gorenstein projective $\tau$-tilting modules in terms of tensor products of modules. As a consequence, we give a class of non-self-injective algebras admitting non-trivial Gorenstein projective $\tau$-tilting…
For a finite dimensional Frobenius cellular algebra, a sufficient and necessary condition for a simple cell module to be projective is given. A special case that dual bases of the cellular basis satisfying a certain condition is also…
This note presents some results on projective modules and the Grothendieck groups K_0 and G_0 for Frobenius algebras and for certain Hopf Galois extensions. Our principal technical tools are the Higman trace for Frobenius algebras and a…
Let $A$ be a coherent algebra and $B$ be a finite-dimensional Gorenstein algebra over a field $k$. We describe finitely presented Gorenstein projective $A\otimes_k B$-modules in terms of their underlying onesided modules. Moreover, if the…
We compute the Grothendieck group K_0 of non-commutative analogues of quantum projective space bundles. Our results specialize to give the Grothendieck groups of non-commutative analogues of projective spaces, and specialize to recover the…
We introduce a complete radical formula for modules over non-commutative rings which is the equivalence of a radical formula in the setting of modules defined over commutative rings. This gives a general frame work through which known…
We generalize to noncommutative cylinder the solution generation technique, originally suggested for gauge theories on noncommutative plane. For this purpose we construct partial isometry operators and complete set of orthogonal projectors…
In this article we study modules over wild canonical algebras which correspond to extension bundles [9] over weighted projective lines. We prove that all modules attached to extension bundles can be established by matrices with coefficients…
In this paper, we study the problem when a finitely generated torsionless module is projective. Let $\Lambda$ be an Artinian local algebra with radical square zero. Then a finitely generated torsionless $\Lambda$-module $M$ is projective if…
In this paper, we investigate noncommutative resolutions of (generalized) AS-Gorenstein isolated singularities. Noncommutative resolutions in graded case are achieved as the graded endomorphism rings of some finitely generated graded…
We describe a novel method for computing sheaf cohomology over weighted projective spaces and stacks using exterior algebra and differential module techniques, generalizing an algorithm due to Eisenbud-Fl\o ystad-Schreyer over projective…
For a tensor ring $T_R(M)$, we obtain sufficient and necessary conditions to describe all complete projective resolutions and all Gorenstein projective modules. As a consequence, we provide a method for constructing Gorenstein projective…
The existence of the Gorenstein projective precovers over arbitrary rings is an open question. It is known that if the ring has finite Gorenstein global dimension, then every module has a Gorenstein projective precover. We prove here a…
This article describes recent applications of algebraic geometry to noncommutative algebra. These techniques have been particularly successful in describing graded algebras of small dimension.