Related papers: Tilting modules over Auslander-Gorenstein Algebras

The aim of this paper is to unify classification theories of torsion classes of finite dimensional algebras and commutative Noetherian rings. For a commutative Noetherian ring $R$ and a module-finite $R$-algebra $\Lambda$, we study the set…

Let $\Gamma$ denote a distance-regular graph with diameter $D \ge 3$. Assume $\Gamma$ has classical parameters $(D,b,\alpha,\beta)$ with $b < -1$. Let $X$ denote the vertex set of $\Gamma$ and let $A \in MX$ denote the adjacency matrix of…

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…

We study homological properties of test modules that are, in principle, modules that detect finite homological dimensions. The main outcome of our results is a generalization of a classical theorem of Auslander and Bridger: we prove that,…

Let $R$ and $S$ be rings and $_R\omega_S$ a semidualizing bimodule. We prove that there exists a Morita equivalence between the class of $\infty$-$\omega$-cotorsionfree modules and a subclass of the class of $\omega$-adstatic modules. Also…

We prove that a finite dimensional algebra is $\tau$-tilting finite if and only if it does not admit large silting modules. Moreover, we show that for a $\tau$-tilting finite algebra $A$ there is a bijection between isomorphism classes of…

We introduce the notion of balanced pair of additive subcategories in an abelian category. We give sufficient conditions under which the balanced pair of subcategories gives rise to equivalent homotopy categories of complexes. As an…

Let T be a tilting module.In this paper, some relative Gorenstein projective and Gortenstein injective modules are studied.

We construct a class of non-weight modules over the twisted $N=2$ superconformal algebra $\T$. Let $\mathfrak{h}=\C L_0\oplus\C G_0$ be the Cartan subalgebra of $\T$, and let $\mathfrak{t}=\C L_0$ be the Cartan subalgebra of even part…

For a Lie-Rinehart algebra (A,L), generators for the Gerstenhaber algebra \Lambda_A L correspond bijectively to right (A,L)-connections on A in such a way that B-V structures correspond to right (A,L)-module structures on A. When L is…

For any increasing function $f: {\Bbb N} \rightarrow {\Bbb N}_{\ge 2}$ which takes only finitely many distinct values, a connected finite dimensional algebra $\Lambda$ is constructed, with the property that $\text{fin.dim}_n\, \Lambda =…

In this paper the authors consider four questions of primary interest for the representation theory of reductive algebraic groups: (i) Donkin's Tilting Module Conjecture, (ii) the Humphreys-Verma Question, (iii) whether $\operatorname{St}_r…

In the first part of this paper the projective dimension of the structural modules in the BGG category $\mathcal{O}$ is studied. This dimension is computed for simple, standard and costandard modules. For tilting and injective modules an…

In this paper we study homological dimensions of finitely generated modules over commutative Noetherian local rings, called reducing homological dimensions. We obtain new characterizations of Gorenstein and complete intersection local rings…

W-algebras are a class of non-commutative algebras related to the classical universal enveloping algebras. They can be defined as a subquotient of U(g) related to a choice of nilpotent element e and compatible nilpotent subalgebra m. The…

A classical theorem of Forster asserts that a finite module $M$ of rank $\leq n$ over a Noetherian ring of Krull dimension $d$ can be generated by $n + d$ elements. We prove a generalization of this result, with "module" replaced by…

Let $\Lambda$ be the path algebra of a finite quiver $Q$ over a finite-dimensional algebra $A$. Then $\Lambda$-modules are identified with representations of $Q$ over $A$. This yields the notion of monic representations of $Q$ over $A$. If…

We show that every two-term tilting complex over an Artin algebra has a tilting module over a certain factor algebra as a homology group. Also, we determine the endomorphism algebra of such a homology group, which is given as a certain…

In this paper we investigate the endomorphism algebras of standard cluster tilting objects in the stably 2-Calabi-Yau categories $\Sub{\Lambda_w}$ with elements $w$ in Coxeter groups in \cite{BIRSc}. They are examples of the 2-Auslander…

Let $\Lambda,\Gamma$ be rings and $R=\left(\begin{array}{cc}\Lambda & 0 \\ M & \Gamma\end{array}\right)$ the triangular matrix ring with $M$ a $(\Gamma,\Lambda)$-bimodule. Let $X$ be a right $\Lambda$-module and $Y$ a right $\Gamma$-module.…