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
- [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
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
