On $p$-permutation equivalences: Between Rickard equivalences and isotypies
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- by Robert Boltje and Bangteng Xu PDF
- Trans. Amer. Math. Soc. 360 (2008), 5067-5087 Request permission
Abstract:
Broué and Rickard defined in their landmark papers from 1990 and 1996 the notions of an isotypy and a splendid equivalence between $p$-blocks of finite groups. Here, we define a notion of equivalence, which we call a $p$-permutation equivalence, that implies an isotypy and is implied by a splendid equivalence. Moreover, we study properties of $p$-permutation equivalences.References
- J. Alperin and Michel BrouĂ©, Local methods in block theory, Ann. of Math. (2) 110 (1979), no. 1, 143â157. MR 541333, DOI 10.2307/1971248
- David Benson, Modular representation theory: new trends and methods, Lecture Notes in Mathematics, vol. 1081, Springer-Verlag, Berlin, 1984. MR 765858
- Robert Boltje, Linear source modules and trivial source modules, Group representations: cohomology, group actions and topology (Seattle, WA, 1996) Proc. Sympos. Pure Math., vol. 63, Amer. Math. Soc., Providence, RI, 1998, pp. 7â30. MR 1603127, DOI 10.1090/pspum/063/1603127
- R. Boltje: Chain complexes for Alperinâs weight conjecture and Dadeâs ordinary conjecture in the abelian defect group case. To appear in J. Group Theory. Available at http://math.ucsc.edu/~boltje/publications.html.
- Robert Boltje and Burkhard KĂŒlshammer, A generalized Brauer construction and linear source modules, Trans. Amer. Math. Soc. 352 (2000), no. 7, 3411â3428. MR 1694281, DOI 10.1090/S0002-9947-00-02530-7
- Robert Boltje and Burkhard KĂŒlshammer, Monomial resolutions of trivial source modules, J. Algebra 248 (2002), no. 1, 146â201. MR 1879012, DOI 10.1006/jabr.2001.8816
- Michel BrouĂ©, On Scott modules and $p$-permutation modules: an approach through the Brauer morphism, Proc. Amer. Math. Soc. 93 (1985), no. 3, 401â408. MR 773988, DOI 10.1090/S0002-9939-1985-0773988-9
- Michel BrouĂ©, IsomĂ©tries parfaites, types de blocs, catĂ©gories dĂ©rivĂ©es, AstĂ©risque 181-182 (1990), 61â92 (French). MR 1051243
- Morton E. Harris, Splendid derived equivalences for blocks of finite groups, J. London Math. Soc. (2) 60 (1999), no. 1, 71â82. MR 1721816, DOI 10.1112/S0024610799007619
- Hirosi Nagao and Yukio Tsushima, Representations of finite groups, Academic Press, Inc., Boston, MA, 1989. Translated from the Japanese. MR 998775
- Jeremy Rickard, Splendid equivalences: derived categories and permutation modules, Proc. London Math. Soc. (3) 72 (1996), no. 2, 331â358. MR 1367082, DOI 10.1112/plms/s3-72.2.331
- Jacques Thévenaz, $G$-algebras and modular representation theory, Oxford Mathematical Monographs, The Clarendon Press, Oxford University Press, New York, 1995. Oxford Science Publications. MR 1365077
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
- Received by editor(s): October 5, 2005
- Published electronically: May 19, 2008
- Additional Notes: The first authorâs research was supported by the NSF, DMS-0200592
- © Copyright 2008
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 360 (2008), 5067-5087
- MSC (2000): Primary 20C20, 20C15, 19A22
- DOI: https://doi.org/10.1090/S0002-9947-08-04393-6
- MathSciNet review: 2415064