Related papers: Morita equivalence for graded rings

A coring (A,C) consists of an algebra A and a coalgebra C in the monoidal category of A-bimodules. Corings and their comodules arise naturally in the study of Hopf-Galois extensions and descent theory, as well as in the study of Hopf…

We show that a bimodule between block algebras which has a fusion stable endopermutation module as a source and which induces Morita equivalences between centralisers of nontrivial subgroups of a defect group induces a stable equivalence of…

Let $G$ be a group and $\Bbbk$ a commutative ring. All categories and functors are assumed to be $\Bbbk$-linear. We define a $G$-invariant bimodule ${}_SM_R$ over $G$-categories $R, S$ and a $G$-graded bimodule ${}_BN_A$ over $G$-graded…

We develop a group graded Morita theory over a G-graded G-acted algebra, where G is a finite group.

We contribute to the classification of finite dimensional algebras under stable equivalence of Morita type. More precisely we give a classification of the class of Erdmann's algebras of dihedral, semi-dihedral and quaternion type and obtain…

We establish a large class of homotopy coherent Morita-equivalences of Dold-Kan type relating diagrams with values in any weakly idempotent complete additive $\infty$-category; the guiding example is an $\infty$-categorical Dold-Kan…

Given Z-graded rings A and B, we study when the categories gr-A and gr-B are equivalent. We relate the Morita-type results of Ahn-Marki and del Rio to the twisting systems introduced by Zhang. Using Z-algebras, we obtain a simple proof of…

Let $E$ and $F$ be finite graphs with no sinks, and $k$ any field. We show that shift equivalence of the adjacency matrices $A_E$ and $A_F$, together with an additional compatibility condition, implies that the Leavitt path algebras…

We characterize the pairs of sup-lattices which occur as pairs of Morita equivalence bimodules between quantales in terms of the mutual relation between the sup-lattices.

We introduce Morita equivalence for Nijenhuis groupoids and for their infinitesimal counterparts, establishing a global-to-infinitesimal correspondence under the Lie functor. A special case is that of holomorphic Lie groupoids and…

Inverse semigroups are the abstract counterparts of pseudogroups of transformations. The abstract counterparts of atlases in differential geometry are what Wagner termed `generalized heaps'. These are sets equipped with a ternary operation…

In this note we recall some recent progress in understanding the representation theory of *-algebras over rings C = R(i) where R is ordered and i^2 = -1. The representation spaces are modules over auxiliary *-algebras with inner products…

We study modular forms of some congruence subgroups. In this paper, we treat the cases level is 2-power, 3-power or 5. Structures of graded rings and many identities of infinite sum or infinite product are given. Theory of rational (1/3,…

We study elementary equivalence of adele rings and decidability for adele rings of general number fields. We prove that elementary equivalence of adele rings implies isomorphism of the adele rings.

The aim of this paper is to give a survey of the theory of bundle gerbes. In our approach we especially emphasize the unifying role of Morita equivalences in this theory. We also discuss a higher analog of Morita bundle gerbes called Morita…

A different proof to a known criterion of derived equivalence implying birationality is given. Derived equivalent smooth projective curves over an algebraically closed field are proved to be isomorphic. A different proof of derived…

Let (G,H) be one of the equal rank reductive dual pairs (Mp_{2n},O_{2n+1}) or (U_n,U_n) over a non-archimedean local field of characteristic zero. It is well-known that the theta correspondence establishes a bijection between certain…

By results of the second author, 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…

The Graded Classification Conjecture states that for finite directed graphs $E$ and $F$, the associated Leavitt path algebras $L_\K(E)$ and $L_\K(F)$ are graded Morita equivalent, i.e., $\Gr L_\K(E) \approx_{\gr} \Gr L_\K(F)$, if and only…

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…