In this paper, we introduce and study five families of Lie groups in degenerate Clifford geometric algebras. These Lie groups preserve the even and odd subspaces and some other subspaces under the adjoint representation and the twisted adjoint representation. The considered Lie groups contain degenerate spin groups, Lipschitz groups, and Clifford groups as subgroups in the case of arbitrary dimension and signature. The considered Lie groups can be of interest for various applications in physics, engineering, and computer science.

中文翻译：

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简并 Clifford 几何代数中的一些李群

在本文中，我们介绍并研究了简并 Clifford 几何代数中李群的五个族。这些李群在伴随表示和扭曲伴随表示下保留偶数和奇数子空间以及一些其他子空间。所考虑的李群包含简并自旋群、Lipschitz 群和 Clifford 群作为任意维数和签名情况下的子群。所考虑的李群可能对物理、工程和计算机科学中的各种应用感兴趣。