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arXiv · 2312.10258

Brauer pairs for splendid Rickard equivalences

Jadyn V. Breland·Sam K. Miller
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Abstract

We define the notion of a Brauer pair of a chain complex, extending the notion of a Brauer pair of a $p$-permutation module introduced by Boltje and Perepelitsky. In fact, the Brauer pairs of a splendid Rickard equivalence $C$ coincide with the set of Brauer pairs of the corresponding $p$-permutation equivalence $Λ(C)$ induced by $C$. As a result, we derive structural results for splendid Rickard equivalences that correspond to known structural properties for $p$-permutation equivalences. In particular, we show splendid Rickard equivalences induce local splendid Rickard equivalences between normalizer block algebras as well as centralizer block algebras.

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Jadyn V. Breland, Sam K. Miller. 2025-12-04. Brauer pairs for splendid Rickard equivalences. https://doi.org/10.1016/j.jalgebra.2025.11.029

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