|
On  -permutation equivalences: Between Rickard equivalences and isotypies
Author(s):
Robert
Boltje;
Bangteng
Xu
Journal:
Trans. Amer. Math. Soc.
360
(2008),
5067-5087.
MSC (2000):
Primary 20C20, 20C15, 19A22
Posted:
May 19, 2008
Retrieve article in:
PDF DVI PostScript
Abstract |
References |
Similar articles |
Additional information
Abstract:
Broué and Rickard defined in their landmark papers from 1990 and 1996 the notions of an isotypy and a splendid equivalence between  -blocks of finite groups. Here, we define a notion of equivalence, which we call a  -permutation equivalence, that implies an isotypy and is implied by a splendid equivalence. Moreover, we study properties of  -permutation equivalences.
References:
-
- [AB79]
- J. L. ALPERIN, M. BROUÉ: Local methods in block theory. Ann. of Math. 110 (1979), 143-157. MR 541333 (80f:20010)
- [Be84]
- D. BENSON: Modular representation theory: New trends and methods. Springer Lecture Notes 1081, Springer-Verlag 1984. MR 765858 (86g:20013)
- [Bo98]
- R. BOLTJE: Linear source modules and trivial source modules. Proc. Sympos. Pure Math. 63 (1998), 7-30. MR 1603127 (99d:20016)
- [Bo01]
- R. BOLTJE: Chain complexes for Alperin's weight conjecture and Dade's ordinary conjecture in the abelian defect group case. To appear in J. Group Theory. Available at http://math.ucsc.edu/˜boltje/publications.html.
- [BK00]
- R. BOLTJE, B. K¨ULSHAMMER: A generalized Brauer construction and linear source modules. Trans. Amer. Math. Soc. 352 (2000), 3411-3428. MR 1694281 (2000j:20017)
- [BK02]
- R. BOLTJE, B. K¨ULSHAMMER: Monomial resolutions of trivial source modules. J. Algebra 248 (2002), 146-201. MR 1879012 (2002j:20018)
- [Br85]
- M. BROUÉ: On Scott modules and
 -permutation modules: An approach through the Brauer morphism. Proc. Amer. Math. Soc. 93 (1985), 401-408. MR 773988 (86d:20010) - [Br90]
- M. BROUÉ: Isométries parfaites, types de blocs, catégories dérivées. Astérisque 181-182 (1990), 61-92. MR 1051243 (91i:20006)
- [Ha99]
- M. HARRIS: Splendid derived equivalences for blocks of finite groups. J. London Math. Soc. 60 (1999), 71-82. MR 1721816 (2000k:20014)
- [NT89]
- H. NAGAO, Y. TSUSHIMA: Representations of finite groups. Academic Press, San Diego 1989. MR 998775 (90h:20008)
- [Ri96]
- J. RICKARD: Splendid equivalences: Derived categories and permutation modules. Proc. London Math. Soc. 72 (1996), 331-358. MR 1367082 (97b:20011)
- [Th95]
- J. THÉVENAZ:
 -algebras and modular representation theory. Oxford University Press 1995. MR 1365077 (96j:20017)
Similar Articles:
Retrieve articles in Transactions of the American Mathematical Society
with MSC
(2000):
20C20, 20C15, 19A22
Retrieve articles in all Journals with MSC
(2000):
20C20, 20C15, 19A22
Additional Information:
Robert
Boltje
Affiliation:
Department of Mathematics, University of California, Santa Cruz, California 95064
Email:
boltje@ucsc.edu
Bangteng
Xu
Affiliation:
Department of Mathematics, University of California, Santa Cruz, California 95064
Address at time of publication:
Department of Mathematics, Eastern Kentucky University, 521 Lancaster Avenue, Wallace 313, Richmond, Kentucky 40475
Email:
btxu@math.ucsc.edu, bangteng.xu@eku.edu
DOI:
10.1090/S0002-9947-08-04393-6
PII:
S 0002-9947(08)04393-6
Received by editor(s):
October 5, 2005
Posted:
May 19, 2008
Additional Notes:
The first author's research was supported by the NSF, DMS-0200592
Copyright of article:
Copyright
2008,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
|
Comments: webmaster@ams.org