On the local structure of Morita and Rickard equivalences between Brauer blocks by Lluis Puig

Cover of: On the local structure of Morita and Rickard equivalences between Brauer blocks | Lluis Puig

Published by Springer in Basel .

Written in English

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Subjects:

  • Finite groups,
  • Representations of groups

Edition Notes

Book details

StatementLluís Puig
SeriesProgress in mathematics -- v. 178, Progress in mathematics (Boston, Mass.) -- v. 178.
Classifications
LC ClassificationsQA177 .P85 1999eb
The Physical Object
Format[electronic resource] /
Pagination1 online resource (260 p.)
Number of Pages260
ID Numbers
Open LibraryOL27078653M
ISBN 103034886934
ISBN 109783034886932, 9783034897327
OCLC/WorldCa828736011

Download On the local structure of Morita and Rickard equivalences between Brauer blocks

Recently, the discovery by Rickard that all blocks with the same cyclic defect group and the same Brauer category have the same homotopic category focussed great interest on the new, loose relationship between blocks called Rickard equivalence.

This book describes the source algebra of a block from the source algebra of a Rickard equivalent. Get this from a library.

On the local structure of Morita and Rickard equivalences between Brauer blocks. [Luis Puig] -- "This book describes the source algebra of a block from the source algebra of a Rickard equivalent block and the source of the Rickard equivalence.

This description requires a new induction procedure. Carreres L.P. () Rickard equivalences between Brauer blocks.

In: On the Local Structure of Morita and Rickard Equivalences between Brauer Blocks. Progress in Mathematics, vol Author: Lluís Puig Carreres.

Get this from a library. On the local structure of Morita and Rickard equivalences between Brauer blocks. [Lluis Puig] -- Brauer had already introduced the defect of a block and opened the way towards a classification by solving all the problems in defects zero and.

Symmetric Groups, Wreath Products, Morita Equivalences, and Broue's Abelian Defect Group Conjecture Article in Bulletin of the London Mathematical Society 34(2) March with 31 Reads.

A local property of basic Morita equivalences. local structure, and induce equivalences between block of the centralizers of subgroups of the defect groups by employing the On the local structure of Morita and Rickard equivalences between Brauer blocks book construction.

A Survey on the Local Structure of Morita and Rickard Equivalences between Brauer Blocks. Representation Theory of Finite Groups: Proceedings of a Special Research Quarter at the Ohio State University, Spring (pp.

Abstract. This paper is a continuation and a completion of the work of the first and the third author on the Jordan decomposition.

We extend the Jordan decomposition of blocks: we show that blocks of finite groups of Lie type in nondescribing characteristic are Morita equivalent to blocks of subgroups associated to isolated elements of the dual group — this is the modular version of a Cited by: L.

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The book is accessible to students who are beginning research in operator algebras after a. Representation Theory of Finite Groups Proceedings of a Special Research Quarter at the Ohio State University, Spring On Blocks and Source Algebras for the Double Covers of the Symmetric Groups.

A Survey on the Local Structure of Morita and Rickard Equivalences between Brauer Blocks. local structure, and induce equivalences between block of the centralizers of subgroups of the defect groups by employing the Brauer construction. Moreover, L. Puig and Y.

Zhou [15], [16] proved that these local equivalences extend to equivalences between blocks Author: Tiberiu Coconet, Andrei Marcus. On the local structure of Morita and Rickard equivalences between Brauer blocks / Lluís Puig.

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Find books. equivalences between two blocks of finite groups are precisely the Morita equivalences arising from an isomorphism of source algebras. Section 5 is devoted to showing that Rouquier’s Rickard complex for blocks with cyclic defect groups constructed in [21] is in fact still splendid in our more restrictive definition of splendid tilting.

On the local structure of Morita and Rickard equivalences between Brauer blocks LluÃ-s Puig. Subgroup complexes Stephen D. Smith. G-algebras and modular representation theory Jacques Thévenaz. Representations of finite and Lie groups Charles B. Thomas. Sporadic groups Discrete groups, expanding graphs, and invariant measures.

Brauer had already introduced the defect of a block and opened the way towards a classification by solving all the problems in defects zero and one, and by providing some evidence for the finiteness of the set of blocks with a given defect.

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We contribute to the classification of finite dimensional algebras under stable equivalence of Morita type. More precisely we give a classification of Erdmann’s algebras of dihedral, semi-dihedral and quaternion type and obtain as byproduct the validity of the Auslander–Reiten conjecture for stable equivalences of Morita type between two algebras, one of which is of dihedral, semi-dihedral Cited by: Groups, Rings and Associated Structures Spa, Belgium j Junecoll.

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Let p be a prime number. This paper solves the question of the structure of the group D(P) of endo-permutation modules over an arbitrary finite p-group P, that was open after Dade’s original papers in ([19], [20]), and it gives a proof of the conjectures proposed in [4] and [10].

This leads to a presentation of D(P) by explicit generators and relations, generalizing the presentation. Abstract. This is a report on advances in the representation theory of finite dimensional algebras in the years – During these years, the German research council (DFG) has sponsered a Forschungsschwerpunkt devoted to the representation theory of finite groups and finite dimensional algebras; it started in and will be finished by Cited by: On blocks of defect two and one simple module, and Lie algebra structure of HH¹.

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This book is the first in a co-edition between the Jean-Morlet Chair at CIRM and the Springer Lecture Notes in Mathematics which aims to collect together courses and lectures on cutting-edge subjects given during the term of the Jean-Morlet Chair, as well as new material produced in its wake.

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Puig: Blocks of Finite Groups Reviewer: 渡辺アツミ, 58(2) pp. Vol No. 3 Index • Book Review R. Kiehl and R. Weissauer: Weil Conjectures, Perverse Sheaves and l'adic Fourier Transform (Ergeb. Math. Grenzgeb. (3), 42).

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