Related papers: Recollements and Gorenstein projective modules for…

We give a characterization of indecomposable exceptional modules over finite dimensional gentle algebras. As an application, we study gentle algebras arising from an unpunctured surface and show that a class of indecomposable modules…

In this paper, we provide a new method for constructing tilting objects in a triangulated category via recollements. The $p$-cycle approach to exceptional curve processes significant advantages in constructing recollements and ladders, due…

Let $V$ be a vertex operator algebra and $g$ an automorphism of finite order. We construct an associative algebra $A_g(V)$ and a pair of functors between the category of $A_g(V)$-modules and a certain category of admissible $g$-twisted…

Reflexive functors of modules naturally appear in Algebraic Geometry. In this paper we define a wide and elementary family of reflexive functors of modules, closed by tensor products and homomorphisms, in which Algebraic Geometry can be…

In this paper, some new characterizations on Gorenstein projective, injective and flat modules over commutative noetherian local ring are given.

Let $\mathbf{k}$ be a field of arbitrary characteristic, and let $\Lambda$ be a finite dimensional $\mathbf{k}$-algebra. In this short note we prove that if $V$ is a finitely generated strongly Gorenstein-projective left $\Lambda$-module…

We show that there is a reflection type bijection between the indecomposable summands of two multiplicity free tilting modules $X$ and $Y$. This bijection fixes the common indecomposable summands of $X$ and $Y$ and sends indecomposable…

Let $R$ a commutative ring, $\mathfrak{a} \subset R$ an ideal, $I$ an injective $R$-module and $S \subset R$ a multiplicatively closed set. When $R$ is Noetherian it is well-known that the $\mathfrak{a}$-torsion sub-module…

Skew-gentle algebras are skew-group algebras of certain gentle algebras endowed with a Z 2-action. Using the topological description of Opper, Plamondon and Schroll in [OPS] for the indecomposable objects of the derived category of any…

We customize the existing models for the bounded derived category of gentle algebras to obtain simple graph theoretic tools to analyze indecomposable objects, Auslander-Reiten triangles, and their interaction with the associated homological…

There are many examples of optimization problems whose associated polyhedra can be described much nicer, and with way less inequalities, by projections of higher dimensional polyhedra than this would be possible in the original space.…

In [F. Caselli, Involutory reflection groups and their models, J. Algebra 24 (2010), 370--393] there is constructed a uniform Gelfand model for all non-exceptional irreducible complex reflection groups which are involutory. Such model can…

An extension $B\subset A$ of finite dimensional algebras is bounded if the $B$-$B$-bimodule $A/B$ is $B$-tensor nilpotent, its projective dimension is finite and $\mathrm{Tor}_i^B(A/B, (A/B)^{\otimes_B j})=0$ for all $i, j\geq 1$. We show…

For $\Lambda$ a selfinjective algebra, and $Q$ a finite quiver without oriented cycles, the algebra $\Lambda Q$ is a Gorenstein algebra and the category ${\rm Gproj}\Lambda Q$ of Gorenstein-projective $\Lambda Q$-modules is a Frobenius…

In this paper, we show that the Gorenstein global dimension of trivial ring extensions is often infinite. Also we study the transfer of Gorenstein properties between a ring and its trivial ring extensions. We conclude with an example…

Motivated by the relation between Schur algebra and the group algebra of a symmetric group, along with other similar examples in algebraic Lie theory, Min Fang and Steffen Koenig addressed some behaviour of the endomorphism algebra of a…

Let $C$ be a semidualizing module. We first investigate the properties of finitely generated $G_C$-projective modules. Then, relative to $C$, we introduce and study the rings of Gorenstein (weak) global dimensions at most 1, which we call…

We study criteria for a ring - or more generally, for a small category - to be Gorenstein and for a module over it to be of finite projective dimension. The goal is to unify the universal coefficient theorems found in the literature and to…

A Lefschetz module is a module over a graded algebra $A$ that satisfies analogues of Poincar\'{e} duality, the Hard Lefschetz property, and the Hodge--Riemann relations with respect to an open convex cone $\mathscr{K}$ in the degree one…

For any ring $R$, we investigate balanced pairs of classes of modules and their relations to cotorsion triples. We characterize the case when a balanced pair generates a tilting cotorsion pair, and dually, when it cogenerates a cotilting…