Titlebook: On the Local Structure of Morita and Rickard Equivalences between Brauer Blocks; Lluís Puig Carreres Book 1999 Springer Basel AG 1999 Equi

特征

,-algebras and ,,-interior algebras,Following Bernhard Keller [13], a ... or, in short, a . is an .-algebra . endowed with a differential .-graded .-module structure (see Remark 10.5 above) such that the product map . ⊗. → . is .-linear or, equivalently, such that, for any ., . ∈ . and any ∈ℱ,we have (cf. 10.2.3)..

Abominate

On the local structure of Hecke ,,-interior algebras,As in Section 15, let . and .’ be finite groups, .. a subgroup of . × .’ and ..a ..-interior algebra, respectively denote by . and .’ the first and the second projection maps for . × .’, and set

官僚统治

Morita stable equivalences between Brauer blocks,e (.’.’). ≅ .’ (.’). as . ’-interior algebras), which restricted to both . (. × 1) and O (1 x .’) is projective. Set . = . and .’ = .’.’,so that .. is also an . ⊗. (.’)°-module, and denote respectively by Mod. and Mod. the categories of .-free .- and .’-modules; it is clear that .. determines a functor from Mod. to Mod., namely the functor

河流

,,-modules,1, here we are interested only on the differential .-graded .-modules which are finitely generated as .-modules (in short, . and it is now clear that they are just the .. In other words, an .-finite complexe of .-modules . is an .-finite .-module endowed with a unitary .-algebra homomorphism

小平面

Congestion

0743-1643 and one, and by providing some evidence for the finiteness of the set of blocks with a given defect. In 1959 he discovered the defect group, and in 1964 Dade determined the blocks with cyclic defect groups..In 1978 Alperin and Broué discovered the Brauer category, and Broué and the author determine

案发地点

Noninjective induction of ,,-interior algebras,struction in the following section to give an alternative description of the ...-interior algebras, which will appear naturally when dealing with Morita equivalences between Brauer blocks in Section 6 below.

syncope

On the local structure of Hecke ,,-interior algebras, on . until Section 16, in order to do it in the more general framework of the ..-interior algebras, except for the contents of Proposition 5.5 and Corollary 5.7 below which will apply to ..-interior algebras as it stands.

Facilities

Introduction,ed successfully in the . [9]. Our first approach had been to switch from virtual characters to “virtual modules” and [22] has to be understood as a contribution to this effort: there we show that, indeed, the “construction” of virtual characters described in [8] and [19] can be performed in full generality with “virtual modules”.

expound

General notation, terminology and quoted results,ificant exception is .-algebras ℱ and . that we introduce in Section 9 and employ in all the subsequent sections. If . is an .-algebra, we denote by Aut(.) the group of automorphisms of ., by .* the group of invertible elements of A, by .(.) the Jacobson radical of ., by Z(.) the center of . and by .° the opposite .-algebra; recall that