On $p$-permutation equivalences: Between Rickard equivalences and isotypies

Rickard Equivalences and Block Theory

De nition We say that a subgroup H of G controls the fusion of p subgroups of G if the following two conditions are ful lled C H contains a Sylow p subgroup Sp of G C whenever P is a subgroup of Sp and g is an element of G such that gPg Sp there exist z in the centralizer CG P of P in G and h in H such that g hz Basic example We denote by Op G the largest normal subgroup of G with order prime t...

Block Theory via Stable and Rickard Equivalences

On Monoidal Equivalences and Ann-equivalences

The equivalence between a monoidal category and a strict one has been proved by some authors such as Nguyen Duy Thuan [8], Christian Kassel [2], Peter Schauenburg [7]. In this paper, we show another proof of the problem by constructing a strict monoidal category M(C) consisting of M -functors and M morphisms of a category C and we prove C is equivalent to it. The proof is based on a basic chara...

Equivalences between stochastic systems

Time-dependent correlation functions of (unstable) particles undergoing biased or unbiased diffusion, coagulation and annihilation are calculated. This is achieved by similarity transformations between different stochastic models and between stochastic and soluble non-stochastic models. The results agree with experiments on one-dimensional annihilationcoagulation processes. PACS: 02.50.Ga, 05.4...

Equivalences between cluster categories

Tilting theory in cluster categories of hereditary algebras has been developed in [BMRRT] and [BMR]. These results are generalized to cluster categories of hereditary abelian categories. Furthermore, for any tilting object T in a hereditary abelian category H, we verify that the tilting functor HomH(T,−) induces a triangle equivalence from the cluster category C(H) to the cluster category C(A),...