Related papers: On Cohen-Macaulay Auslander algebras
One of the first remarkable results in the representation theory of artin algebras, due to Auslander and Ringel-Tachikawa, is the characterization of when an artin algebra is representation-finite. In this paper, we investigate aspects of…
We show that endomorphism rings of cogenerators in the module category of a finite-dimensional algebra A admit a canonical tilting module, whose tilted algebra B is related to A by a recollement. Let M be a gen-finite A-module, meaning…
For an Artinian $(n-1)$-Auslander algebra $\Lambda$ with global dimension $n(\geq 2)$, we show that if $\Lambda$ admits a trivial maximal $(n-1)$-orthogonal subcategory of $\mod\Lambda$, then $\Lambda$ is a Nakayama algebra and the…
In this paper we study a certain class of central extensions of preprojective algebras of quivers under the name quiver Heisenberg algebras (QHA). There are several classes of algebras introduced before by different researchers from…
We study the degeneration problem for maximal Cohen-Macaulay modules and give several examples of such degenerations. It is proved that such degenerations over an even-dimensional simple hypersurface singularity of type $(A_n)$ are given by…
We give characterizations of Gorenstein projective, Gorenstein flat and Gorenstein injective modules over the group algebra for large families of infinite groups and show that every weak Gorenstein projective, weak Gorenstein flat and weak…
We define Khovanov-Lauda-Rouquier subalgebras which are generalizations of redotted versions of Webster's tensor product algebras of type $A_1$. Quotient algebras of these subalgebras are isomorphic to Webster's tensor product algebras in…
In this paper, we introduce and study a class of algebras which we call ada algebras. An artin algebra is ada if every indecomposable projective and every indecomposable injective module lies in the union of the left and the right parts of…
In this paper we study generalized Gorenstein Arf rings; a class of one-dimensional Cohen-Macaulay local Arf rings that is strictly contained in the class of Gorenstein rings. We obtain new characterizations and examples of Arf rings, and…
This is an English translation of the author's Ph.D. thesis, accumulating his results on a construction of Cohen-Macaulay modules over a polynomial ring that appeared in the study of Cauchy-Fueter equations. This construction is generalized…
Let $\Lambda$ be an $n$-Auslander algebra with global dimension $n+1$. In this paper, we prove that $\Lambda$ is representation-finite if and only if the number of non-isomorphic indecomposable $\Lambda$-modules with projective dimension…
Weighted projective lines, introduced by Geigle and Lenzing in 1987, are important objects in representation theory. They have tilting bundles, whose endomorphism algebras are the canonical algebras introduced by Ringel. The aim of this…
We introduce a new family of algebras, called Serre-formal algebras. They are Iwanaga-Gorenstein algebras for which applying any power of the Serre functor on any indecomposable projective module, the result remains a stalk complex. Typical…
We consider a finite acyclic quiver $\mathcal{Q}$ and a quasi-Frobenius ring $R$. We endow the category of quiver representations over $R$ with a model structure, whose homotopy category is equivalent to the stable category of…
In 1996, Doty, Nakano and Peters defined infinitesimal Schur algebras, combining the approach via polynomial representations with the approach via $G_r T$-modules to representations of the algebraic group $G = \mathrm{GL}_n$. We study…
In this paper, we examine the class of cofibrant modules over a group algebra $kG$, that were defined by Benson in [2]. We show that this class is always the left-hand side of a complete hereditary cotorsion pair in the category of…
Let $(R, \m)$ be a $d$-dimensional commutative noetherian local ring. Let $\M$ denote the morphism category of finitely generated $R$-modules and let $\Sc$ be the submodule category of $\M$. In this paper, we specify the Auslander transpose…
We show that Artin-Schelter regularity of a $\mathbb{Z}$-graded algebra can be examined by its associated $\mathbb{Z}^r$-graded algebra. We prove that there is exactly one class of four-dimensional Artin-Schelter regular algebras with two…
Auslander conjectured that every Artin algebra satisfies a certain condition on vanishing of cohomology of finitely generated modules. The failure of this conjecture - by a 2003 counterexample due to Jorgensen and Sega - motivates the…
We define algebras of quasi-quaternion type, which are symmetric algebras of tame representation type whose stable module category has certain structure similar to that of the algebras of quaternion type introduced by Erdmann. We observe…