Derived equivalence in $SL_2(p^2)$
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- by Joseph Chuang
- Trans. Amer. Math. Soc. 353 (2001), 2897-2913
- DOI: https://doi.org/10.1090/S0002-9947-01-02679-4
- Published electronically: March 14, 2001
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Abstract:
We present a proof that Broué’s Abelian Defect Group Conjecture is true for the principal $p$-block of the group $SL_2(p^2)$. Okuyama has independently obtained the same result using a different approach.References
- J. L. Alperin, Local representation theory, Cambridge Studies in Advanced Mathematics, vol. 11, Cambridge University Press, Cambridge, 1986. Modular representations as an introduction to the local representation theory of finite groups. MR 860771, DOI 10.1017/CBO9780511623592
- Michel Broué, Isométries parfaites, types de blocs, catégories dérivées, Astérisque 181-182 (1990), 61–92 (French). MR 1051243
- M. Broué, Rickard equivalences and block theory, Groups ’93 Galway/St. Andrews, Vol. 1 (Galway, 1993) London Math. Soc. Lecture Note Ser., vol. 211, Cambridge Univ. Press, Cambridge, 1995, pp. 58–79. MR 1342782, DOI 10.1017/CBO9780511629280.009
- Jon F. Carlson, The cohomology of irreducible modules over $\textrm {SL}(2,\,p^{n})$, Proc. London Math. Soc. (3) 47 (1983), no. 3, 480–492. MR 716799, DOI 10.1112/plms/s3-47.3.480
- J. Carlson and R. Rouquier, Self-equivalences of stable module categories, Math. Z. 233 (2000), 165–178.
- Guoqiang Huang, On extended block induction, J. Algebra 185 (1996), no. 3, 886–904. MR 1419728, DOI 10.1006/jabr.1996.0355
- T. Okuyama, Some examples of derived equivalent blocks of finite groups, preprint.
- Jeremy Rickard, The abelian defect group conjecture, Proceedings of the International Congress of Mathematicians, Vol. II (Berlin, 1998), 1998, pp. 121–128. MR 1648062
- —, Bousfield localization for representation theorists, preprint.
- Jeremy Rickard, Derived categories and stable equivalence, J. Pure Appl. Algebra 61 (1989), no. 3, 303–317. MR 1027750, DOI 10.1016/0022-4049(89)90081-9
- Jeremy Rickard, Morita theory for derived categories, J. London Math. Soc. (2) 39 (1989), no. 3, 436–456. MR 1002456, DOI 10.1112/jlms/s2-39.3.436
- Jeremy Rickard, Derived equivalences as derived functors, J. London Math. Soc. (2) 43 (1991), no. 1, 37–48. MR 1099084, DOI 10.1112/jlms/s2-43.1.37
- Jeremy Rickard, Splendid equivalences: derived categories and permutation modules, Proc. London Math. Soc. (3) 72 (1996), no. 2, 331–358. MR 1367082, DOI 10.1112/plms/s3-72.2.331
Bibliographic Information
- Joseph Chuang
- Affiliation: St. John’s College, Oxford OX1 3JP, UK
- Address at time of publication: School of Mathematics, University of Bristol, University Walk, Bristol BS8 1TW, UK
- Email: joseph.chuang@bristol.ac.uk
- Received by editor(s): March 3, 1999
- Received by editor(s) in revised form: January 24, 2000
- Published electronically: March 14, 2001
- © Copyright 2001 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 353 (2001), 2897-2913
- MSC (2000): Primary 20C20
- DOI: https://doi.org/10.1090/S0002-9947-01-02679-4
- MathSciNet review: 1828478