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The Lie group is not required to be compact. More generally, we study spaces of invariant sections in homogeneous vector bundles, and take a special interest in the case where the fibres are algebras. These latter cases have a natural global algebra structure. We classify these automorphic algebras for the case where the homogeneous space has compact stabilisers. This work has applications in the theoretical development of geometric deep learning and also in the theory of automorphic Lie algebras.<\/jats:p>","DOI":"10.1007\/s10444-024-10126-7","type":"journal-article","created":{"date-parts":[[2024,4,11]],"date-time":"2024-04-11T12:01:56Z","timestamp":1712836916000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Computing equivariant matrices on homogeneous spaces for geometric deep learning and automorphic Lie algebras"],"prefix":"10.1007","volume":"50","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5320-0490","authenticated-orcid":false,"given":"Vincent","family":"Knibbeler","sequence":"first","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2024,4,11]]},"reference":[{"key":"10126_CR1","doi-asserted-by":"crossref","unstructured":"Kutyniok, G.: The Mathematics of Artificial Intelligence. 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