相关论文: Singular equivalence and the (Fg) condition

For a finite quiver $Q$, we study the reachability category $\mathbf{Reach}_Q$. We investigate the properties of $\mathbf{Reach}_Q$ from both a categorical and a topological viewpoint. In particular, we compare $\mathbf{Reach}_Q$ with…

Inspired by the properties of an $n$-frame of gradients $(\nabla f_1, \ldots, \nabla f_n)$ of a Morin map $f:M\rightarrow\mathbb{R}^n$, with $\dim M\geq n$, we introduce the notion of Morin singularities in the context of singular…

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…

In this paper, we extend the study of graded equivalences to the case of general idempotent graded rings. We prove that the existence of a graded equivalence between two categories of graded torsion-free unital modules may be characterized…

We prove that the classes of graph algebras, Exel-Laca algebras, and ultragraph algebras coincide up to Morita equivalence. This result answers the long-standing open question of whether every Exel-Laca algebra is Morita equivalent to a…

Necessary and sufficient conditions are obtained for the uniqueness of standard regular AF masas in regular limit algebras up to approximate inner unitary equivalence.

Let G < SL(V) be a finite group, V is finite dimensional over a field F, p=char F and S(V) is the symmetric algebra of V. We determine when the subring of G-invariants S(V)^G is a polynomial ring. As a consequence, we classify, if F is…

We prove that two finite-dimensional commutative algebras over an algebraically closed field are isomorphic if and only if they give rise to isomorphic representations of the category of finite sets and surjective maps.

Let $\mathcal{A}= \{A_t \}_{t \in G}$ and $\mathcal{B}= \{B_t \}_{t\in G}$ be $C^*$-algebraic bundles over a finite group $G$. Let $C=\oplus_{t \in G}A_t$ and $D=\oplus_{t\in G}B_t$. Also, let $A=A_e$ and $B=B_e$, where $e$ is the unit…

The classical Morita Theorem for rings established the equivalence of three statements, involving categorical equivalences, isomorphisms between corners of finite matrix rings, and bimodule homomorphisms. A fourth equivalent statement…

We associate with every pure flag simplicial complex $\Delta$ a standard graded Gorenstein $\mathbb{F}$-algebra $R_{\Delta}$ whose homological features are largely dictated by the combinatorics and topology of $\Delta$. As our main result,…

We show that infinitely many Gorenstein weakly-exceptional quotient singularities exist in all dimensions, we prove a weak-exceptionality criterion for five-dimensional quotient singularities, and we find a sufficient condition for being…

We classify all $2$-blocks with abelian defect groups of rank $4$ up to Morita equivalence. The classification holds for blocks over a suitable discrete valuation ring as well as for those over an algebraically closed field. An application…

We observe that a finitely generated algebraic algebra R (over a field) is finite dimensional if and only if the associated graded ring grR is right noetherian, if and only if grR has right Krull dimension, if and only if grR satisfies a…

We introduce Morita and Rickard equivalences over a group graded G-algebra between block extensions. A consequence of such equivalences is that Sp\"ath's central order relation holds between two corresponding character triples.

This paper studies self-injective algebras of polynomial growth. We prove that the derived equivalence classification of weakly symmetric algebras of domestic type coincides with the classification up to stable equivalences (of Morita…

We describe cohomological conditions that are necessary and sufficient for the existence of balanced dualizing dg-modules, generalizing a theorem of Van den Bergh for balanced dualizing complexes over graded algebras. As a consequence, we…

We study $F$-graded systems of ideals in $R$, which are sequences of ideals giving rise to Cartier algebras on $R$. We identify how properties of these systems (or modifications of these systems) affect the singularity properties of the…

In this paper we prove a general theorem about congruences between automorphic forms on a reductive group G which is compact at infinity modulo the center. If the rank is one, this essentially reduces to Ribet's level-raising theorem. We…

For a discrete valuation ring $R$ with quotient field $K$ and residue field $F$ both of characteristic not 2, we study low-dimensional quadratic forms with Witt class in the $n$-th power of the fundamental ideal of $F$ resp. $K$ and point…