Geodesic
BLOCKS WITH A QUATERNION DEFECT GROUP OVER A 2-ADIC RING: THE CASE Ã4
Glasgow mathematical journal, Tome 49 (2007) no. 1, pp. 29-43

Voir la notice de l'article provenant de la source Cambridge University Press

Except for blocks with a cyclic or Klein four defect group, it is not known in general whether the Morita equivalence class of a block algebra over a field of prime characteristic determines that of the corresponding block algebra over a p-adic ring. We prove this to be the case when the defect group is quaternion of order 8 and the block algebra over an algebraically closed field k of characteristic 2 is Morita equivalent to kÃ4. The main ingredients are Erdmann's classification of tame blocks [6] and work of Cabanes and Picaronny [4, 5] on perfect isometries between tame blocks.
DOI : 10.1017/S0017089507003394
Mots-clés : 20C20 
HOLM, THORSTEN; KESSAR, RADHA; LINCKELMANN, MARKUS. BLOCKS WITH A QUATERNION DEFECT GROUP OVER A 2-ADIC RING: THE CASE Ã4. Glasgow mathematical journal, Tome 49 (2007) no. 1, pp. 29-43. doi: 10.1017/S0017089507003394
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[1] 1.Broué, M., Isométries parfaites, types de blocs, catégories dérivées, Astérisque 181–182 (1990), 61–92. Google Scholar

[2] 2.Broué, M., Isométries de caractères et equivalences de Morita ou dérivées, Publ. Math. IHES 71 (1990), 45–63. Google Scholar | DOI

[3] 3.Broué, M. and Puig, L., A Frobenius theorem for blocks, Invent. Math. 56 (1980), 117–128. Google Scholar

[4] 4.Cabanes, M. and Picaronny, C., Types of blocks with dihedral or quaternion defect groups, J. Fac. Sci. Univ. Tokyo 39 (1992), 141–161. Google Scholar

[5] 5.Cabanes, M. and Picaronny, C., Corrected version of: Types of blocks with dihedral or quaternion defect groups, http://www.math.jussieu.fr/~cabanes/printlist.html (1999). Google Scholar

[6] 6.Erdmann, K., Blocks of tame representation type and related algebras, Lecture Notes in Mathematics No. 1428 (Springer-Verlag, 1990). Google Scholar

[7] 7.Feit, W., The representation theory of finite groups (North-Holland, Amsterdam, 1982). Google Scholar

[8] 8.Puig, L., Nilpotent blocks and their source algebras, Invent. Math. 93 (1988), 77–116. Google Scholar | DOI

[9] 9.Thévenaz, J., G-algebras and modular representation theory (Oxford University Press, 1995). Google Scholar

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