Year: 2026
Type: preprint
Abstract: Let $(K,\mathcal{O},k)$ be a large enough $2$-modular system. We construct two nilpotent block algebras of finite groups which are isomorphic as $\mathcal{O}$-algebras and are Morita equivalent via a bimodule with an endotrivial source of $\mathcal{O}$-rank $3$, but which are not globally isotypic. Hence they are not $2$-permutation equivalent and not splendidly Rickard equivalent. These results separate Morita equivalences with endopermutation source from $p$-permutation equivalences and splendid Rickard equivalences, and also separate almost global isotypies from global isotypies.
Source: arXiv (Cornell University)
Author: Huang, Xin
Language: English
Topic: Finite Group Theory Research
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7204961678