### A note on the basic Morita equivalences SpringerLink ### Dec 20,2013·Puig L.On the local structure of Morita and Rickard equivalences between Brauer blocks.In Progress in Mathematics,vol.178.Basel Birkhäuser,1999,97–100.MATH Google Scholar 5.Puig L,Zhou Y.A local property of basic Morita equivalences.Math Z,2007,256 551–562 Cited by 2Publish Year 2014Author XueQin HuA local property of basic Morita equivalences SpringerLink

### Dec 22,2006·5.Puig L.(1999).On the local structure of Morita and Rickard equivalences between Brauer blocks.Prog.Math.178 261 MathSciNet Google Scholar Cited by 16Publish Year 2007Author Lluis Puig,Yuanyang ZhouBasic Morita stable equivalences between Brauer blocks

### As we say in the introduction,in all the known situations where O has characteristic zero and M..defines a Morita stable equivalence between b and b’,it turns out that σ and σ’ are both bijective and that P..stabilizes by conjugation an O-basis of S..- that is to say,S..is a so-called Dade P..-algebra (cf.2.2) - which implies that p does not divide rank o (N.. Author Lluís Puig CarreresPublish Year 1999On stable equivalences of Morita type SpringerLink

### Oct 16,2006·In section 2 we recall from  the basic properties of Broué's notion of a stable equivalence of Morita type,apply them to p-groups in section 3 and develop some further formal properties in section 4.In the last section we come back to derived equivalences and show,how the tilting complexes for blocks with dihedral defect groups (that Cited by 12Publish Year 1998Author Markus LinckelmannA note on the basic Morita equivalences Request PDF

### Request PDF A note on the basic Morita equivalences Let G and G' be two finite groups,and p be a prime number.k is an algebraically closed field of characteristic p.We denote by b and b A note on the basic Morita equivalences - NASA/ADS

### adshelp[at]cfa.harvard.edu The ADS is operated by the Smithsonian Astrophysical Observatory under NASA Cooperative Agreement NNX16AC86A Basic Rickard equivalences between Brauer blocks

### Abstract.As announced in the introduction,in this last section we consider a particular kind of Rickard equivalences between blocks which,at least conjecturally,seems to be very frequent and which includes the case of the basic Morita equivalences discussed in Section 7.We keep all the notation of Section 18; in particular,M..is an indecomposable D(G × G’)-module associated with b Basic Morita equivalences and isotypies - ScienceDirect

### Sep 01,2020·Basic Morita equivalences and isotypies between blocks are due to L.Puig and M.Broué respectively.In this paper,we prove that a basic Morita equivalence between blocks induces an isotypy if and only if the value at an element u ⋅ ⋅ of the character of a source of the bimodule inducing the basic Morita equivalence is ± m u ⋅ ⋅,where m u ⋅ ⋅ is the multiplicity of the indecomposable direct A note on stable equivalences of Morita type - CORE

### equivalence,is part of a stable equivalence of Morita type if and only if HomΛ(M,Λ) is a projective left Γ-module.The basic strategy,as in Rickard’s proof,is to apply the theory of adjoint functors to −⊗Λ MΓ and its left adjoint.In fact we will see that,just as in the self-injectivecase,theexactfunctorsgivenbytensoringwiththetwo A note on stable equivalences of Morita type

### These stable equivalences of Morita type are,by definition,given by a pair of bimodules that are projective on either side,and the equivalences are induced by a pair of adjoint functors between A note on stable equivalences of Morita type - ScienceDirect

### Feb 01,2007·An inverse equivalence is provided by the functor Hom Λ ( P,−) mod - Λ → mod - Δ.Note that this equivalence also induces a full embedding of stable categories mod ¯ - Δ ↪ mod ¯ - Λ.Now suppose that Γ is stably equivalent to Λ and that e ′,P Γ ′ and Δ ′ A local property of basic Morita equivalences Request PDF

### This is used in our main result,Theorem 6.8 below,where we prove that a basic graded Morita equivalence between OGb and OG ′ b ′ induces a basic graded equivalence at local levels.This is a Group graded basic Morita equivalences - ScienceDirect

### ·In order to state the second main result of this paper,which will be discussed in Section 5,we recall from ,the definition of basic group graded Morita equivalences between stable block algebras.For the rest of this paper,if A is any subgroup in a group G ,we denote by Δ ( A × A ) the diagonal subgroup of A × A . Derived equivalences and stable equivalences of Morita

### We note that to every derived always induces a stable equivalence of Morita type.However,in [HX10],many basic questions on the stable functor remain.For instance,we even don't know AN ALGEBRAIC MODEL FOR RATIONAL TORUS

### The skeleton proof has three parts a Morita equivalence,a Koszul duality and a rigidity argument.The form of the Morita equivalence is fairly standard,but the other two parts have unusual features.2.A.Preparatory Morita equivalences.The basic Morita equivalence states that if A CONSTRUCTIONS OF STABLE EQUIVALENCES OF MORITA

### STABLE EQUIVALENCES OF MORITA TYPE 569 Definition 2.1.Let A and B be two (arbitrary) k-algebras.We say that A and B are stably equivalent of Morita type if there exist an A–B-bimodule AM B and a B–A-bimodule BN A such that (1) M and N are projective as one-sided modules,and (2) M ⊗ B N A⊕P as A–A-bimodules for some projective A–A-bimodule P,and N ⊗ A M B ⊕Q as B–B A local property of basic Rickard equivalences Request PDF

### It turns out that this extended Brauer quotient is an important tool for generalizing some results regarding basic Morita equivalences and basic Rickard equivalences between blocks of finite Block Extensions,Local Categories and Basic Morita

### 9 Group-graded basic Morita equivalences.In the final section we prove the statements of Theorem 1.2.We show that if there is a group-graded basic Morita equivalence between two block extensions,then their extended local categories are preserved. On iterated almost n-stable derived equivalences

### they are all preserved by stable equivalences of Morita type.So,this also helps us to compare the homological dimensions of derived equivalent algebras.For more information about stable equivalences of Morita type,we refer to the papers [3,9,10,7].Let us ﬁrst recall the deﬁnition of almost n-stable derived equivalences.Let F Db(A) ! MORITA THEORY IN ABELIAN,DERIVED

### These notes are based on lectures given at the Workshop on Structured ring spectra and their applications.This workshop took place January 21-25,2002,at the University of Glasgow and was organized by Andy Baker and Birgit Richter.Contents 1.Introduction 1 2.Morita theory in abelian categories 2 3.Morita theory in derived categories 6 3.1. 12345Next