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BLOCKS WITH A QUATERNION DEFECT GROUP OVER A 2-ADIC RING: THE CASE Ã4

Published online by Cambridge University Press:  01 January 2007

THORSTEN HOLM ,
RADHA KESSAR  and
MARKUS LINCKELMANN
THORSTEN HOLM
Affiliation:
Department of Pure Mathematics, University of Leeds, Leeds, LS2 9JT, U.K.
RADHA KESSAR
Affiliation:
Department of Mathematical Sciences, Meston Building, Aberdeen, AB24 3UE, U.K. e-mail: linckelm@maths.abdn.ac.uk
MARKUS LINCKELMANN
Affiliation:
Department of Mathematical Sciences, Meston Building, Aberdeen, AB24 3UE, U.K. e-mail: linckelm@maths.abdn.ac.uk
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Abstract.

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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.

Keywords

20C20
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 49 , Issue 1 , January 2007 , pp. 29 - 43
Copyright
Copyright © Glasgow Mathematical Journal Trust 2007

References

REFERENCES

1.Broué, M., Isométries parfaites, types de blocs, catégories dérivées, Astérisque 181–182 (1990), 61–92.Google Scholar
2.Broué, M., Isométries de caractères et equivalences de Morita ou dérivées, Publ. Math. IHES 71 (1990), 45–63.CrossRefGoogle Scholar
3.Broué, M. and Puig, L., A Frobenius theorem for blocks, Invent. Math. 56 (1980), 117–128.Google Scholar
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.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.Erdmann, K., Blocks of tame representation type and related algebras, Lecture Notes in Mathematics No. 1428 (Springer-Verlag, 1990).Google Scholar
7.Feit, W., The representation theory of finite groups (North-Holland, Amsterdam, 1982).Google Scholar
8.Puig, L., Nilpotent blocks and their source algebras, Invent. Math. 93 (1988), 77–116.CrossRefGoogle Scholar
9.Thévenaz, J., G-algebras and modular representation theory (Oxford University Press, 1995).Google Scholar