Related papers: Splendid Morita equivalences for principal blocks …

This paper is a continuation and a completion of [BoRo1]. We extend the Jordan decomposition of blocks: we show that blocks of finite groups of Lie type in non-describing characteristic are Morita equivalent to blocks of subgroups…

We show that a bimodule of two block algebras of finite groups which has an endopermutation module as a source and which induces a stable equivalence of Morita type gives rise, via slash functors, to a family of bimodules of local block…

We consider $p$-blocks with abelian defect groups and in the first part prove a relationship between its Loewy length and that for blocks of normal subgroups of index $p$. Using this, we show that if $B$ is a $2$-block of a finite group…

For $G$ a finite group, $k$ a field of prime characteristic $p$, and $S$ a Sylow $p$-subgroup of $G$, the Sylow permutation module $\mathrm{Ind}^G_S(k)$ plays a role in diverse facets of representation theory and group theory, ranging from…

We show that every block of the category of cuspidal generalized weight modules with finite dimensional generalized weight spaces over the Lie algebra sp(2n)(C) is equivalent to the category of finite dimensional…

We determine the universal deformation ring R(G,V) of certain mod 2 representations V of a finite group G which belong to a 2-modular block of G whose defect groups are isomorphic to a generalized quaternion group D. We show that for these…

We prove that the Eaton-Moreto conjecture is true for the principal blocks of the p-solvable groups

We take advantage of the correspondence between pseudogroups and inverse quantal frames, and of the recent description of Morita equivalence for inverse quantal frames in terms of biprincipal bisheaves, to define Morita equivalence for…

We calculate examples of Picard groups for 2-blocks with abelian defect groups with respect to a complete discrete valuation ring. These include all blocks with abelian 2-groups of 2-rank at most three with the exception of the principal…

We consider the equivalence from the stable module category to a subcategory $\mathcal{L}_A$ of the homotopy category constructed by Kato. This equivalence induces a correspondence between distinguished triangles in the homotopy category…

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…

A finite tensor category is called pointed if all its simple objects are invertible. We find necessary and sufficient conditions for two pointed semisimple categories to be dual to each other with respect to a module category. Whenever the…

We show that two flat commutative Hopf algebroids are Morita equivalent if and only if they are weakly equivalent and if and only if there exists a principal bibundle connecting them. This gives a positive answer to a conjecture due to…

In this paper we investigate blocks of symmetric groups of weight 2 over fields of odd characteristic $p$. We develop an algorithm that relates the quivers of two such blocks forming a $(2:1)$ pair, as introduced by Scopes. We then apply…

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.

In this paper we prove equivalences of categories relating the derived category of a block of the category of representations of a connected reductive algebraic group over an algebraically closed field of characteristic $p$ bigger than the…

We introduce a new notion of Morita equivalence for diffeological groupoids, generalising the original notion for Lie groupoids. For this we develop a theory of diffeological groupoid actions, -bundles and -bibundles. We define a notion of…

Given a field $K$ equipped with a set of discrete valuations $V$, we develop a general theory to relate reduction properties of skew-hermitian forms over a quaternion $K$-algebra $Q$ to quadratic forms over the function field $K(Q)$…

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…

Linckelmann and Murphy have classified the Morita equivalence classes of p-blocks of finite groups whose basic algebra has dimension at most 12. We extend their classification to dimension 13 and 14. As predicted by Donovan's Conjecture, we…