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arXiv · 2608.31083

Morita equivalent blocks with an endotrivial source that are not globally isotypic

Xin Huang
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Abstract

Let $(K,\mathcal{O},k)$ be a large enough $2$-modular system. We show that there is a block algebra $B$ of $\mathcal{O}{\rm SU}_3(2)$ which is Morita equivalent to $\mathcal{O} Q_8$ via a bimodule with a $3$-dimensional endotrivial source. We also prove that $B$ and $\mathcal{O} Q_8$ are not globally isotypic. Hence they are not $p$-permutation equivalent and not splendidly Rickard equivalent.

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BibTeXRIS

Xin Huang. 2026-08-31. Morita equivalent blocks with an endotrivial source that are not globally isotypic. https://arxiv.org/abs/2608.31083

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