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## Development of the method of averaging in Clifford geometric algebras

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Open AccessFeature PaperArticle

Development of the Method of Averaging in Clifford Geometric Algebras

by

1,2

1

HSE University, Myasnitskaya Str. 20, Moscow 101000, Russia

2

Institute for Information Transmission Problems of Russian Academy of Sciences, Bolshoy Karetny Per. 19, Moscow 127051, Russia

*Mathematics* **2023**, *11*(16), 3607; https://doi.org/10.3390/math11163607

Received: 29 June 2023 / Revised: 15 August 2023 / Accepted: 17 August 2023 / Published: 21 August 2023

(This article belongs to the Special Issue Applications of Geometric Algebra)

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We develop the method of averaging in Clifford (geometric) algebras suggested by the author in previous papers. We consider operators constructed using two different sets of anticommuting elements of real or complexified Clifford algebras. These operators generalize Reynolds operators from the representation theory of finite groups. We prove a number of new properties of these operators. Using the generalized Reynolds operators, we give a complete proof of the generalization of Pauli’s theorem to the case of Clifford algebras of arbitrary dimension. The results can be used in geometry, physics, engineering, computer science, and other applications.