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math.RT2025
A reduction theorem for non-vanishing of Hochschild cohomology of block algebras and Happel's property
Patrick Serwene, Constantin-Cosmin Todea
In this short research note we obtain a reduction theorem for the non-vanishing of the first Hochschild cohomology of block algebras of finite groups with non-trivial defect groups…
math.RT2024
Weight conjectures for Parker--Semeraro fusion systems
Radha Kessar, Jason Semeraro, Patrick Serwene +1
We prove that the Parker--Semeraro systems satisfy six of the nine Kessar--Linckelmann--Lynd--Semeraro weight conjectures for saturated fusion systems. As a by-product we obtain th…