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On Some Lie Groups in Degenerate Geometric Algebras

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Advanced Computational Applications of Geometric Algebra (ICACGA 2022)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13771))

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Abstract

In this paper, we introduce and study several Lie groups in degenerate (Clifford) geometric algebras. These Lie groups preserve the even and odd subspaces under the adjoint representation and the twisted adjoint representation. The considered Lie groups are interesting for the study of spin groups and their generalizations in degenerate case.

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Notes

  1. 1.

    It would be of interest to study the relation between the results of this paper and such concepts as the Classification Scheme of Lie groups, the root systems of the Lie groups in degenerate and non-degenerate cases, the Universal enveloping algebras of the Lie algebras.

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Acknowledgements

This work is supported by the Russian Science Foundation (project 21-71-00043), https://rscf.ru/en/project/21-71-00043/.

The authors are grateful to the three anonymous reviewers for their careful reading of the paper and helpful comments on how to improve the presentation.

Author information

Authors and Affiliations

  1. HSE University, 101000, Moscow, Russia

    Ekaterina Filimoshina & Dmitry Shirokov

  2. Institute for Information Transmission Problems of the Russian Academy of Sciences, 127051, Moscow, Russia

    Dmitry Shirokov

Authors
  1. Ekaterina Filimoshina
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  2. Dmitry Shirokov
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Corresponding author

Correspondence to Ekaterina Filimoshina .

Editor information

Editors and Affiliations

  1. Algemetric, Colorado Springs, CO, USA

    David W. Silva

  2. International Christian University, Tokyo, Japan

    Eckhard Hitzer

  3. TU Darmstadt, Darmstadt, Germany

    Dietmar Hildenbrand

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Filimoshina, E., Shirokov, D. (2024). On Some Lie Groups in Degenerate Geometric Algebras. In: Silva, D.W., Hitzer, E., Hildenbrand, D. (eds) Advanced Computational Applications of Geometric Algebra. ICACGA 2022. Lecture Notes in Computer Science, vol 13771. Springer, Cham. https://doi.org/10.1007/978-3-031-34031-4_16

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  • DOI: https://doi.org/10.1007/978-3-031-34031-4_16

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-34030-7

  • Online ISBN: 978-3-031-34031-4

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