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On Picard groups of blocks of finite groups

Boltje, R., Kessar, R. ORCID: 0000-0002-1893-4237 & Linckelmann, M. (2020). On Picard groups of blocks of finite groups. Journal of Algebra, 558, pp. 70-101. doi: 10.1016/j.jalgebra.2019.02.045


We show that the subgroup of the Picard group of ap-block ofa finite group given by bimodules with endopermutation sources modulo theautomorphism group of a source algebra is determined locally in terms of thefusion system on a defect group. We show that the Picard group of a block overa complete discrete valuation ringOof characteristic zero with an algebraicclosurekofFpas residue field is a colimit of finite Picard groups of blocks overp-adic subrings ofO. We apply the results to blocks with an abelian defectgroup and Frobenius inertial quotient, and specialise this further to blockswith cyclic or Klein four defect groups.

Publication Type: Article
Additional Information: © Elsevier 2020. This manuscript version is made available under the CC-BY-NC-ND 4.0 license
Subjects: Q Science > QA Mathematics
Departments: School of Science & Technology > Mathematics
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Text - Accepted Version
Available under License Creative Commons Attribution Non-commercial No Derivatives.

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