On Grade Automorphism in Ternary Clifford Algebras

Филимошина Е. Р., Широков Д. С., , in: Volume 267: International Conference on Machine Learning, 13-19 July 2025, Vancouver Convention Center, Vancouver, CanadaVol. 267.: [б.и.], 2025. P. 17153–17188.

Добавлено: 28 октября 2025 г.

Determinant, Characteristic Polynomial, and Inverse in Commutative Analogues of Clifford Algebras

Sharma H., Широков Д. С., Advances in Applied Clifford Algebras 2025 Vol. 35 Article 44

Добавлено: 2 октября 2025 г.

Generalized Degenerate Clifford and Lipschitz Groups in Geometric Algebras

Филимошина Е. Р., Широков Д. С., Advances in Applied Clifford Algebras 2025 Vol. 35 Article 29

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 ...

Добавлено: 29 мая 2025 г.

On Unitary Groups in Ternary and Generalized Clifford Algebras

Широков Д. С., Advances in Applied Clifford Algebras 2025 Vol. 35 Article 25

Добавлено: 20 мая 2025 г.

On SU(3) in Ternary Clifford Algebra

Широков Д. С., , in: Advances in Computer Graphics: 41st Computer Graphics International Conference, CGI 2024, Geneva, Switzerland, July 1–5, 2024, Proceedings, Part IIIVol. 15340.: Springer, 2025. P. 336–348.

Добавлено: 1 апреля 2025 г.

Generalized Degenerate Clifford and Lipschitz Groups

Филимошина Е. Р., Dmitry Shirokov, , in: Advances in Computer Graphics: 41st Computer Graphics International Conference, CGI 2024, Geneva, Switzerland, July 1–5, 2024, Proceedings, Part IIIVol. 15340.: Springer, 2025. P. 364–376.

Добавлено: 1 апреля 2025 г.

Calculation of Spin Group Elements Revisited

Широков Д. С., International Journal of Geometric Methods in Modern Physics 2026 Vol. 23 No. 5 Article 2540031

Добавлено: 5 декабря 2024 г.

On Rank of Multivectors in Geometric Algebras

Dmitry Shirokov, Mathematical Methods in the Applied Sciences 2025 Vol. 48 No. 11 P. 11095–11102

Добавлено: 4 декабря 2024 г.

Introducing Multidimensional Dirac–Hestenes Equation

Sofia Rumyantseva, Широков Д. С., Advances in Applied Clifford Algebras 2025 Vol. 35 Article 24

Добавлено: 8 ноября 2024 г.

A Note on Centralizers and Twisted Centralizers in Clifford Algebras

Филимошина Е. Р., Широков Д. С., Advances in Applied Clifford Algebras 2024 Vol. 34 Article 50

Добавлено: 8 ноября 2024 г.

On SVD and Polar Decomposition in Real and Complexified Clifford Algebras

Широков Д. С., Advances in Applied Clifford Algebras 2024 Vol. 34 Article 23

In this paper, we present a natural implementation of singular value decomposition (SVD) and polar decomposition of an arbitrary multivector in nondegenerate real and complexified Clifford geometric algebras of arbitrary dimension and signature. The new theorems involve only operations in geometric algebras and do not involve matrix operations. We naturally define these and other related ...

Добавлено: 23 августа 2024 г.

On Some Lie Groups in Degenerate Geometric Algebras

Филимошина Е. Р., Широков Д. С., , in: Advanced Computational Applications of Geometric Algebra: First International Conference, ICACGA 2022, Denver, CO, USA, October 2-5, 2022, ProceedingsVol. 13771.: Springer, 2024. P. 186–198.

Добавлено: 3 февраля 2024 г.

On Singular Value Decomposition and Polar Decomposition in Geometric Algebras

Широков Д. С., , in: Advances in Computer Graphics: 40th Computer Graphics International Conference, CGI 2023, Shanghai, China, August 28 – September 1, 2023, Proceedings, Part IV* 4. Vol. 14498.: Springer, 2024. P. 391–401.

Добавлено: 25 декабря 2023 г.

Development of the method of averaging in Clifford geometric algebras

Широков Д. С., Mathematics 2023 Vol. 11 No. 16 Article 3607

Добавлено: 5 октября 2023 г.

On Noncommutative Vieta Theorem in Geometric Algebras

Dmitry Shirokov, , in: Empowering Novel Geometric Algebra for Graphics and Engineering. 7th International Workshop, ENGAGE 2022, Virtual Event, September 12, 2022, Proceedings.: Cham: Springer, 2023. P. 28–37.

Добавлено: 19 августа 2023 г.

On Some Lie Groups in Degenerate Clifford Geometric Algebras

Ekaterina Filimoshina, Dmitry Shirokov, Advances in Applied Clifford Algebras 2023 Vol. 33 Article 44

Добавлено: 19 августа 2023 г.

Noncommutative Vieta theorem in Clifford geometric algebras

Dmitry Shirokov, Mathematical Methods in the Applied Sciences 2024 Vol. 47 No. 14 P. 11305–11320

Добавлено: 2 апреля 2023 г.

On generalization of Lipschitz groups and spin groups

Ekaterina Filimoshina, Dmitry Shirokov, Mathematical Methods in the Applied Sciences 2024 Vol. 47 No. 3 P. 1375–1400

Добавлено: 11 октября 2022 г.

Basis-free Formulas for Characteristic Polynomial Coefficients in Geometric Algebras

Kamron Abdulkhaev, Широков Д. С., Advances in Applied Clifford Algebras 2022 Vol. 32 No. 5 Article 57

Добавлено: 11 октября 2022 г.

On solutions of the Yang-Mills equations in the algebra of h-forms

Широков Д. С., , in: Journal of Physics: Conference Series, Volume 2099Vol. 2099: International Conference «Marchuk Scientific Readings 2021» (MSR-2021) 4-8 October 2021, Novosibirsk, Russian Federation.: IOP Publishing, 2021. Ch. 012015 P. 1–7.

Добавлено: 11 октября 2022 г.