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Arbitrarily large Morita Frobenius numbers
Florian Eisele, Michael Livesey
We construct blocks of finite groups with arbitrarily large Morita Frobenius numbers, an invariant which determines the size of the minimal field of definition of the associated ba…
Donovan's conjecture and extensions by the centralizer of a defect group
Charles W. Eaton, Michael Livesey
We consider Donovan's conjecture in the context of blocks of groups with defect group and normal subgroups such that , extending similar results…
Linear source invertible bimodules and Green correspondence
Markus Linckelmann, Michael Livesey
We show that the Green correspondence induces an injective group homomorphism from the linear source Picard group of a block of a finite group algebra to the l…
On Picent for blocks with normal defect group
Michael Livesey, Claudio Marchi
We prove that if is a block of a finite group with normal abelian defect group and inertial quotient a direct product of elementary abelian groups, then $\operatorname{Picent}(…
On Picard groups of blocks with normal defect groups
Michael Livesey
Let be a block with normal abelian defect group and abelian inertial quotient. We prove that every Morita auto-equivalence of has linear source. We note that this improves…
Some examples of Picard groups of blocks
Charles W. Eaton, Michael Livesey
We calculate examples of Picard groups for 2-blocks with abelian defect groups with respect to a complete discrete valuation ring. These include all blocks with abelian 2-groups of…