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Book Review

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Book Information

Author(s): 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, $98.00, ISBN 3-7643-6156-5

References:

[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, ``$G$-algebras and modular representation theory'', Oxford Math. Monographs, Clarendon Press, Oxford, 1995. MR 96j:20017

Additional Information:

Reviewer(s):
Jacques Thévenaz
Affiliation: Université de Lausanne
Email: Jacques.Thevenaz@ima.unil.ch

Review Information:
Journal: Bull. Amer. Math. Soc. 38 (2001), 97-100.

MSC (2000): Primary 20C20
PII: S 0273-0979(00)00885-5
Posted: October 2, 2000
Additional notes: This review is an expanded version of a review in French which appeared in the {\it Gazette des Mathématiciens}.
Copyright of article: Copyright 2000, American Mathematical Society

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