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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
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
Corresponding
E-mail address:
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Abstract.

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 4. 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

Type
Research Article
Copyright
Copyright © Glasgow Mathematical Journal Trust 2007

References

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6.Erdmann, K., Blocks of tame representation type and related algebras, Lecture Notes in Mathematics No. 1428 (Springer-Verlag, 1990).Google Scholar
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8.Puig, L., Nilpotent blocks and their source algebras, Invent. Math. 93 (1988), 77116.CrossRefGoogle Scholar
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