Computing equivariant matrices on homogeneous spaces for geometric deep learning and automorphic Lie algebras-Reference-Cited by-同舟云学术

Computing equivariant matrices on homogeneous spaces for geometric deep learning and automorphic Lie algebras

Published:2024-04 Issue:2 Volume:50 Page:
ISSN:1019-7168
Container-title:Advances in Computational Mathematics
language:en
Short-container-title:Adv Comput Math

Author:

Knibbeler Vincent^ORCID

Abstract

AbstractWe develop an elementary method to compute spaces of equivariant maps from a homogeneous space G/H of a Lie group G to a module of this group. 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.

Funder

London Mathematical Society

Publisher

Springer Science and Business Media LLC

Link

https://link.springer.com/content/pdf/10.1007/s10444-024-10126-7.pdf

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