Related papers: Yoneda algebras and their singularity categories

Duality properties are studied for a Gorenstein algebra that is finite and projective over its center. Using the homotopy category of injective modules, it is proved that there is a local duality theorem for the subcategory of acyclic…

In this article we develop formal category theory within augmented virtual double categories. Notably we formalise the classical notions of Kan extension, Yoneda embedding $\text y_A\colon A \to \hat A$, exact square, total category and…

We show that the bigroupoid of separable symmetric Frobenius algebras over an algebraically closed field and the bigroupoid of finitely semi-simple Calabi-Yau categories are equivalent. To this end, we construct a trace on the category of…

We define $A_{\infty}$-structures -- algebras, coalgebras, modules, and comodules -- in an arbitrary monoidal DG category or bicategory by rewriting their definitions in terms of unbounded twisted complexes. We develop new notions of strong…

By results of Rognerud, a source algebra equivalence between two $p$-blocks of finite groups induces an equivalence between the categories of cohomological Mackey functors associated with these blocks, and a splendid derived equivalence…

Let $Q$ be a finite quiver and $\Lambda$ be the radical square zero algebra of $Q$ over a field. We give a full and dense functor from the category of reduced differential projective modules over $\Lambda$ to the category of representations…

This paper is devoted to the study of graded associative algebras that satisfy a graded polynomial identity of degree $2$. % Let $\mathsf{G}$ be a finite abelian group, $\mathbb{F}$ a field of characteristic zero and $\mathfrak{A}$ a…

Let $\Gamma$ be a group acting on a scheme $X$ and on a Lie superalgebra $\mathfrak{g}$, both defined over an algebraically closed field of characteristic zero $\Bbbk$. The corresponding equivariant map superalgebra $M(\mathfrak{g},…

We prove that for any $\mathbb{N}$-graded Gorenstein tiled order $A$, the stable category $\underline{\mathrm{CM}}^{\mathbb{Z}}A$ is triangle equivalent to the perfect derived category of the incidence algebra of a finite poset…

We give sufficient conditions for a Frobenius category to be equivalent to the category of Gorenstein projective modules over an Iwanaga-Gorenstein ring. We then apply this result to the Frobenius category of special Cohen-Macaulay modules…

From the notion of (co)generator in relative homological algebra, we present the concept of finite balanced system $[(\mathcal{X} , \omega ); (\nu, \mathcal{Y})]$ as a tool to induce balanced pairs $(\mathcal{X} , \mathcal{Y} )$ for the…

Let $\Lambda$ be a $\mathbb{Z}$-graded artin algebra. Two classical results of Gordon and Green state that if $\Lambda$ has only finitely many indecomposable gradable modules, up to isomorphism, then $\Lambda$ has finite representation…

We propose a new framework for the study of homological properties for (compactly generated) triangulated categories such as regularity, finiteness of global or finitistic dimension, gorensteinness or injective generation and the relation…

Let ${\mathfrak g}$ be a complex semisimple Lie algebra, and $Y_h({\mathfrak g})$, $U_q(L{\mathfrak g})$ the corresponding Yangian and quantum loop algebra, with deformation parameters related by $q=\exp(\pi i h)$. When $h$ is not a…

We show that the class of twisted fractionally Calabi-Yau algebras of finite global dimension coincides with the stable endomorphism algebras of $d$-cluster tilting modules over $d$-representation-finite algebras. This is an application of…

In this paper we define and study triangulated categories in which the Hom-spaces have Krull dimension at most one over some base ring (hence they have a natural 2-step filtration), and each factor of the filtration satisfies some…

Given a tagged triangulation of a once-punctured polygon $P^*$ with $n$ vertices, we associate an ice quiver with potential such that the frozen part of the associated frozen Jacobian algebra has the structure of a Gorenstein $K[X]$-order…

Finite-dimensional Jacobian algebras are studied from the perspective of representation types. We establish that (like other representation types) the notions of $E$-finiteness and $E$-tameness are invariant under mutations of quivers with…

Let $\Lambda$ be a finite dimensional algebra. Let $\mathcal C$ be a functorially finite exact subcategory of $\Lambda$-mod with enough projective and injective objects and $\mathcal S (\mathcal C)$ be its monomorphism category. It turns…

Consider a $k$-linear Frobenius category $\mathscr{E}$ with a projective generator such that the corresponding stable category $\mathscr{C}$ is 2-Calabi--Yau, Hom-finite with split idempotents. Let $l,m\in\mathscr{C}$ be maximal rigid…