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

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Lluís Puig Carreresers have met several times in Darm- stadt at the Computer Graphics Center. In these meetings they discussed the essential issues inherent in applying virtual reality to industrial appli- cations and exchanged t978-3-642-46849-0978-3-642-46847-6Series ISSN 1431-1380

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On the Local Structure of Morita and Rickard Equivalences between Brauer Blocks

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dominant

Hecke ,,-interior algebras and noninjective induction,maps the trivial element of .’ on itself and all the others elements on zero; recall that, since . is surjective, we identify . for any O(G × G’)-interior algebra .. (cf. 3.3), and moreover we consider . as an OG-interior algebra.

dysphagia

Basic Morita stable equivalences between Brauer blocks,-basis in .., is a consequence of the following general (and surprising!) result. Recall that a .-form .: . → . of an .-free .-algebra . is an .-linear map fulfilling .(.’) = .(.’a) for any .’ ∈ . and inducing an .-module isomorphism . ? Hom.(.) which maps a ∈ . on the .-form mapping .’ ∈ . on .(.’)

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Induction of ,,-interior algebras,ity functor and . times the “restriction-induction” throughout the trivial subgroup - has to be replaced by a more sophisticated functor on .-interior algebras consisting of the “direct sum” of the identity functor and . times a “direct sum of restriction-inductions”involving the family of all the p