52 research outputs found
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On duality inducing automorphisms and sources of simple modules in classical groups
Bounds for Hochschild cohomology of block algebras
We show that for any block algebra B of a finite group over an algebraically
closed field of prime characteristic the dimension of HH^n(B) is bounded by a
function depending only on the nonnegative integer n and the defect of B. The
proof uses in particular a theorem of Brauer and Feit which implies the result
for n=0.Comment: 6 page
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Crossover morita equivalences for blocks of the covering groups of the symmetric and alternating groups
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Blocks with quaternion defect group over a 2-adic ring: the case \tilde{A}_4
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 . The main ingredients are Erdmann's classification of tame blocks and work of Cabanes and Picaronny on perfect isometries between tame blocks
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A reduction theorem for fusion systems of blocks
Let k be an algebraically closed field of characteristic p and G a finite group. An interesting question for fusion systems is whether they can be obtained from the local structure of a block of the group algebra kG. In this paper we develop some methods to reduce this question to the case when G is a central p′-extension of a simple group. As an application of our result, we obtain that the ‘exotic’ examples of fusion systems discovered by Ruiz and Viruel [A. Ruiz, A. Viruel, The classification of p-local finite groups over the extra-special group of order p3 and exponent p, Math. Z. 248 (2004) 45–65] do not occur as fusion systems of p-blocks of finite groups
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