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String algebras over local rings: admissibility and biseriality.

Raphael Bennett-Tennenhaus (Aarhus University)
Wednesday 15 November 2023 16:15–17:15 Koll. G4 (1532-222)
Mathematics Seminar

String algebras are classically of path algebras over fields. Path algebras have also been considered over any noetherian local ground ring. Raggi-Cardenas and Salmeron generalised the definition of an admissible ideal in this context. A generalisation of string algebras from my PhD thesis likewise replaced the ground field with a local ring. In this talk I will explain how this definition relates to admissibility, and yields biserial rings in a sense used by Kirichenko and Yaremenko. I will also provide examples coming from metastable homotopy theory following work of Baues and Drozd. Time permitted, I will present an example of a clannish algebra over a local ring that is related to modular representations of the Matheiu 11-group, following Roggenkamp. This is based on an arxiv preprint 2305.12885.

Organised by: AarHomAlg
Contact: Raphael, Amit Revised: 09.11.2023