arXiv subjects

E. R. Filimoshina

Publications and source records attributed to E. R. Filimoshina.

5 recordsLinked to original sources

arXiv2026

On Lie Groups Preserving Subspaces of Degenerate Clifford Algebras

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.

math.RA↗

arXiv2025

Generalized Degenerate Clifford and Lipschitz Groups in Geometric Algebras

This paper introduces and studies generalized degenerate Clifford and Lipschitz groups in geometric (Clifford) algebras. These Lie groups preserve the direct sums of the subspaces determined by the grade involution and reversion under the adjoint and twisted adjoint representations in degenerate geometric algebras. We prove that the generalized degenerate Clifford and Lipschitz groups can be defined using centralizers and twisted centralizers of fixed grades subspaces and the norm functions that are widely used in the theory of spin groups. We study the relations between these groups and consider them in the particular cases of plane-based geometric algebras and Grassmann algebras. The corresponding Lie algebras are studied. The presented groups are interesting for the study of generalized degenerate spin groups and applications in computer science, physics, and engineering.

math.RA↗

arXiv2024

A Note on Centralizers and Twisted Centralizers in Clifford Algebras

This paper investigates centralizers and twisted centralizers in degenerate and non-degenerate Clifford (geometric) algebras. We provide an explicit form of the centralizers and twisted centralizers of the subspaces of fixed grades, subspaces determined by the grade involution and the reversion, and their direct sums. The results can be useful for applications of Clifford algebras in computer science, physics, and engineering.

math.RA↗

arXiv2024

On Some Lie Groups in Degenerate Clifford Geometric Algebras

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.

math.RA↗

arXiv2022

On generalization of Lipschitz groups and spin groups

This paper presents some new Lie groups preserving fixed subspaces of geometric algebras (or Clifford algebras) under the twisted adjoint representation. We consider the cases of subspaces of fixed grades and subspaces determined by the grade involution and the reversion. Some of the considered Lie groups can be interpreted as generalizations of Lipschitz groups and spin groups. The Lipschitz groups and the spin groups are subgroups of these Lie groups and coincide with them in the cases of small dimensions. We study the corresponding Lie algebras.

math-ph↗