# On Lie Groups Preserving Subspaces of Degenerate Clifford Algebras

arXiv: https://arxiv.org/abs/2601.07191 · HTML: https://mlsanity.com/paper/2601.07191/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 49 references that are in the map.
- First posted on arXiv 12 Jan 2026.

## Builds on (most cited first, 6 of 6)

- [Clifford Neural Layers for PDE Modeling](https://mlsanity.com/paper/2209.04934/) (2022)
- [Clifford Group Equivariant Neural Networks](https://mlsanity.com/paper/2305.11141/) (2023)
- [Geometric Algebra Transformer](https://mlsanity.com/paper/2305.18415/) (2023)
- [Geometric Clifford Algebra Networks](https://mlsanity.com/paper/2302.06594/) (2023)
- [Clifford-Steerable Convolutional Neural Networks](https://mlsanity.com/paper/2402.14730/) (2024)
- [Graded Symmetry Groups: Plane and Simple](https://mlsanity.com/paper/2107.03771/) (2021)

## Abstract (arXiv)

This paper introduces Lie groups in degenerate geometric (Clifford) algebras that preserve four fundamental subspaces determined by the grade involution and reversion under the adjoint and twisted adjoint representations. We prove that these Lie groups can be equivalently defined using norm functions of multivectors applied in the theory of spin groups. We also study the corresponding Lie algebras. Some of these Lie groups and algebras are closely related to Heisenberg Lie groups and algebras. The introduced groups are interesting for various applications in physics and computer science, in particular, for constructing equivariant neural networks.