Related papers: On iterated almost $\nu$-stable derived equivalenc…
We give a new proof, by using simplified terminology and notation, to a result of Puig stating that if a bimodule of two block algebras of finite groups over an algebraically closed field induces a stable equivalence of Morita type and has…
A.S. Dugas and R. Mart\'{i}nez-Villa proved in \cite[Corollary 5.1]{dm} that if there exists a stable equivalence of Morita type between the $k$-algebras $\Lambda$ and $\Gamma$, then it is possible to replace $\Lambda$ by a Morita…
The Nakayama conjecture states that an algebra of infinite dominant dimension should be self-injective. Motivated by understanding this conjecture in the context of derived categories, we study dominant dimensions of algebras under derived…
Let $k$ be an algebraically closed field. It is known that any stable equivalence between standard representation-finite self-injective $k$-algebras (without block of Loewy length 2) lifts to a standard derived equivalence, in particular,…
In this brief postscript to our paper "Integral transforms and Drinfeld centers in derived algebraic geometry", we describe a Morita equivalence for derived, categorified matrix algebras implied by theory developed since its appearance. We…
In this paper, we introduce $\Phi$-Auslander-Yoneda algebras in a triangulated category with $\Phi$ a parameter set in $\mathbb N$, and provide a method to construct new derived equivalences between these $\Phi$-Auslander-Yoneda algebras…
In this note, we prove that stable equivalences of Morita type between blocks of finite groups induce identification of certain quotient fusion systems under sone assumption. We also collect some related results for separable equivalences.
We give a unified generalization of Dugas' construction on stable auto-equivalences of Morita type from local symmetric algebras to arbitrary symmetric algebras. For group algebras $kP$ of $p$-groups in characteristic $p$, we recover all…
In this paper, we show that stable functors of derived equivalences preserve the isomorphism classes of versal deformation rings of finitely generated Gorenstein-projective modules over finite dimensional $k$-algebras. Then we generalize…
We define $\Delta$-equivalence for dual operator systems and prove that it is an equivalence relation. We show that weak TRO-equivalence of dual operator spaces induces a stable isomorphism between them which is given by multiplication with…
We give a proof, based on the rigidity of tilting complexes, that the class of self-injective finite-dimensional algebras over an algebraically closed field is closed under derived equivalence.
In this paper we introduce a new property for normed algebras. This property which we call it stability, plays a key role in the studying of the theory of almost multiplier maps. In this note we study some of the basic properties of this…
We give a general construction of realization functors for $t$-structures on the base of a strong stable derivator. In particular, given such a derivator $\mathbb D$, a $t$-structure $\mathbf t=(\mathcal D^{\leq0},\mathcal D^{\geq0})$ on…
We provide a far reaching derived equivalence classification of the cluster-tilted algebras of Dynkin type D and suggest standard forms for the derived equivalence classes. We believe that the classification is complete, but some subtle…
Let $A$ and $B$ be finite-dimensional $k$-algebras over a field $k$ such that $A/\rad(A)$ and $B/\rad(B)$ are separable. In this note, we consider how to transfer a stable equivalence of Morita type between $A$ and $B$ to that between $eAe$…
We give a new proof, by using the terminology and notation in the textbook \cite{Lin18b}, to a result, due to Puig, stating that a stable equivalence of Morita type between two block algebras of finite groups induced by a bimodule with an…
We obtain strong invariance principles for normalized multiple iterated sums and integrals of the form $\bbS_N^{(\nu)}(t)=N^{-\nu/2}\sum_{0\leq k_1<...<k_\nu\leq Nt}\xi(k_1)\otimes\cdots\otimes\xi(k_\nu)$, $t\in[0,T]$ and…
The Nakayama permutations of two derived equivalent, self-injective Artin algebras are conjugate. A different but elementary approach is given to showing that the weak symmetry and self-injectivity of finite-dimensional algebras over an…
Since 2005 a new powerful invariant of an algebra emerged using earlier work of Horv\'ath, H\'ethelyi, K\"ulshammer and Murray. The authors studied Morita invariance of a sequence of ideals of the centre of a finite dimensional algebra over…
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…