Book Review

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Book Information:

Author: Lluis Puig

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

Additional book information: Progress in Math., vol. 178, Birkhäuser, Basel, 1999, 261 pp., ISBN 3-7643-6156-5, $98.00

**[B1]**M. Broué, Equivalences between block algebras: an introduction, in ``Finite dimensional algebras and related topics'', Kluwer Academic, Dordrecht, Netherlands, 1994, pp. 1-26. MR**97c:20004****[B2]**M. Broué, Rickard equivalences and block theory, in ``Groups '93 Galway - St. Andrews'', London Math. Soc. Lecture Notes Series 211, Cambridge Univ. Press, 1995, pp. 58-79. MR**96d:20011****[KZ]**S. König, A. Zimmermann, ``Derived equivalences for group rings'', Lecture Notes in Math. 1685, Springer Verlag, Berlin, 1998. MR**2000g:16018****[L1]**M. Linckelmann, The isomorphism problem for cyclic blocks and their source algebras,*Invent. Math.***125**(1996), 265-283. MR**97h:20010****[L2]**M. Linckelmann, The source algebras of blocks with a Klein four defect group,*J. Algebra***167**(1994), 821-854. MR**95h:20014****[P1]**L. Puig, Pointed groups and construction of characters,*Math. Z.***176**(1981), 209-216. MR**82d:20015****[P2]**L. Puig, Nilpotent blocks and their source algebras,*Invent. Math.***93**(1988), 77-116. MR**89e:20023****[P3]**L. Puig, Algèbres de source de certains blocs des groupes de Chevalley,*Astérisque***181-182**(1990), 221-236. MR**92e:20007****[P4]**L. Puig, On Joanna Scopes' criterion of equivalence for blocks of symmetric groups,*Algebra Colloq.***1**(1994), 25-55. MR**95f:20020****[Ri1]**J. Rickard, Derived equivalences as derived functors,*J. London Math. Soc.***43**(1991), 37-48. MR**92b:16043****[Ri2]**J. Rickard, Splendid equivalences: Derived categories and permutation modules,*Proc. London Math. Soc.***72**(1996), 331-358. MR**97b:20011****[Th]**J. Thévenaz, ``-algebras and modular representation theory'', Oxford Math. Monographs, Clarendon Press, Oxford, 1995. MR**96j:20017**

Review Information:

Reviewer: Jacques Thévenaz

Affiliation: Université de Lausanne

Email: Jacques.Thevenaz@ima.unil.ch

Journal: Bull. Amer. Math. Soc.

**38**(2001), 97-100

MSC (2000): Primary 20C20

Published electronically: October 2, 2000

Additional Notes: This review is an expanded version of a review in French which appeared in the Gazette des Mathématiciens.

Review copyright: © Copyright 2000 American Mathematical Society