发现退化克利福德代数中保持四个子空间的李群，可由多向量范数定义。
On Lie Groups Preserving Subspaces of Degenerate Clifford Algebras
- 通过多向量范数重构保持子空间的李群
- 揭示部分群与海森堡群的紧密联系
- 为构建等变神经网络提供理论支持
本文研究退化几何（克利福德）代数中的李群，这些群在伴随表示和扭曲伴随表示下保持由阶反演和逆转决定的四个基本子空间。证明了这些李群可通过多向量的范数函数等价定义，进而推广至旋群理论。同时研究了相应的李代数，发现其中一些群与代数与海森堡李群及代数密切相关。所引入的群在物理与计算机科学中具有广泛应用价值，尤其适用于构建等变神经网络。
原文摘要 · Abstract (English)
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.
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