All Stories

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

    Article • Advances in Applied Clifford Algebras, August 2025, Springer Science + Business Media

    Dmitry Shirokov

  2. On Unitary Groups in Ternary and Generalized Clifford Algebras

    Article • Advances in Applied Clifford Algebras, May 2025, Springer Science + Business Media

    Dmitry Shirokov

  3. On Rank of Multivectors in Geometric Algebras

    Article • Mathematical Methods in the Applied Sciences, April 2025, Wiley

    Dmitry Shirokov

  4. Calculation of spin group elements revisited

    Article • International Journal of Geometric Methods in Modern Physics, March 2025, World Scientific Pub Co Pte Lt

    Dmitry Shirokov

  5. Generalized Degenerate Clifford and Lipschitz Groups

    Article • January 2025, Springer Science + Business Media

    Dmitry Shirokov

  6. On Multidimensional Dirac–Hestenes Equation in Geometric Algebra

    Article • January 2025, Springer Science + Business Media

    Dmitry Shirokov

  7. On SU(3) in Ternary Clifford Algebra

    Article • January 2025, Springer Science + Business Media

    Dmitry Shirokov

  8. On SVD and Polar Decomposition in Real and Complexified Clifford Algebras

    Article • Advances in Applied Clifford Algebras, May 2024, Springer Science + Business Media

    Dmitry Shirokov

  9. On Some Lie Groups in Degenerate Geometric Algebras

    Article • January 2024, Springer Science + Business Media

    Dmitry Shirokov

  10. On Singular Value Decomposition and Polar Decomposition in Geometric Algebras

    Article • December 2023, Springer Science + Business Media

    Dmitry Shirokov

  11. Development of the Method of Averaging in Clifford Geometric Algebras

    Article • Mathematics, August 2023, MDPI AG

    Dmitry Shirokov

  12. Classification of all constant solutions of SU(2) Yang–Mills equations with arbitrary current in pseudo-Euclidean space ℝp,q

    Article • Modern Physics Letters A, July 2023, World Scientific Pub Co Pte Lt

    Dmitry Shirokov

  13. Noncommutative Vieta theorem in Clifford geometric algebras

    Article • Mathematical Methods in the Applied Sciences, March 2023, Wiley

    Dmitry Shirokov

  14. On Noncommutative Vieta Theorem in Geometric Algebras

    Article • January 2023, Springer Science + Business Media

    Dmitry Shirokov

  15. Basis-Free Formulas for Characteristic Polynomial Coefficients in Geometric Algebras

    Article • Advances in Applied Clifford Algebras, September 2022, Springer Science + Business Media

    Dmitry Shirokov

  16. On generalization of Lipschitz groups and spin groups

    Article • Mathematical Methods in the Applied Sciences, July 2022, Wiley

    Dmitry Shirokov

  17. Hyperbolic Singular Value Decomposition in the Study of Yang–Mills and Yang–Mills–Proca Equations

    Article • Computational Mathematics and Mathematical Physics, June 2022, Pleiades Publishing Ltd

    Dmitry Shirokov

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

    Article • Journal of Physics Conference Series, November 2021, Institute of Physics Publishing

    Dmitry Shirokov

  19. Basis-free Solution to Sylvester Equation in Clifford Algebra of Arbitrary Dimension

    Article • Advances in Applied Clifford Algebras, September 2021, Springer Science + Business Media

    Dmitry Shirokov

  20. A note on the hyperbolic singular value decomposition without hyperexchange matrices

    Article • Journal of Computational and Applied Mathematics, August 2021, Elsevier

    Dmitry Shirokov

  21. On computing the determinant, other characteristic polynomial coefficients, and inverse in Clifford algebras of arbitrary dimension

    Article • Computational and Applied Mathematics, June 2021, Springer Science + Business Media

    Dmitry Shirokov

  22. On Inner Automorphisms Preserving Fixed Subspaces of Clifford Algebras

    Article • Advances in Applied Clifford Algebras, April 2021, Springer Science + Business Media

    Dmitry Shirokov

  23. A note on subspaces of fixed grades in Clifford algebras

    Article • January 2021, American Institute of Physics

    Dmitry Shirokov

  24. On Explicit Formulas for Characteristic Polynomial Coefficients in Geometric Algebras

    Article • January 2021, Springer Science + Business Media

    Dmitry Shirokov

  25. On Some Equations Modeling the Yang–Mills Equations

    Article • Physics of Particles and Nuclei, July 2020, Pleiades Publishing Ltd

    Dmitry Shirokov

  26. On constant solutions of SU(2) Yang-Mills equations with arbitrary current in Euclidean space ℝn

    Article • Journal of Nonlinear Mathematical Physics, January 2020, Springer Science + Business Media

    Dmitry Shirokov

  27. On Basis-Free Solution to Sylvester Equation in Geometric Algebra

    Article • January 2020, Springer Science + Business Media

    Dmitry Shirokov

  28. Calculation of Elements of Spin Groups Using Method of Averaging in Clifford’s Geometric Algebra

    Article • Advances in Applied Clifford Algebras, May 2019, Springer Science + Business Media

    Dmitry Shirokov

  29. Covariantly Constant Solutions of the Yang–Mills Equations

    Article • Advances in Applied Clifford Algebras, May 2018, Springer Science + Business Media

    Dmitry Shirokov

  30. Clifford Algebras and Their Applications to Lie Groups and Spinors

    Article • Geometry Integrability and Quantization, January 2018, Prof. Marin Drinov Academic Publishing House

    Dmitry Shirokov

  31. Classification of Lie algebras of specific type in complexified Clifford algebras

    Article • Linear and Multilinear Algebra, September 2017, Taylor & Francis

    Dmitry Shirokov

  32. General Solutions of One Class of Field Equations

    Article • Reports on Mathematical Physics, December 2016, Elsevier

    Dmitry Shirokov

  33. Constant Solutions of Yang-Mills Equations and Generalized Proca Equations

    Article • Journal of Geometry and Symmetry in Physics, January 2016, Prof. Marin Drinov Academic Publishing House

    Dmitry Shirokov

  34. On Some Lie Groups Containing Spin Group in Clifford Algebra

    Article • Journal of Geometry and Symmetry in Physics, January 2016, Prof. Marin Drinov Academic Publishing House

    Dmitry Shirokov

  35. Method of Averaging in Clifford Algebras

    Article • Advances in Applied Clifford Algebras, December 2015, Springer Science + Business Media

    Dmitry Shirokov

  36. Свертки по рангам и кватернионным типам в алгебрах Клиффорда

    Article • Вестник Самарского государственного технического университета Серия Физико-математические науки, January 2015, Samara State Technical University

    Dmitry Shirokov

  37. Symplectic, Orthogonal and Linear Lie Groups in Clifford Algebra

    Article • Advances in Applied Clifford Algebras, December 2014, Springer Science + Business Media

    Dmitry Shirokov

  38. Calculation of Elements of Spin Groups Using Generalized Pauli’s Theorem

    Article • Advances in Applied Clifford Algebras, June 2014, Springer Science + Business Media

    Dmitry Shirokov

  39. Pauli theorem in the description of n-dimensional spinors in the Clifford algebra formalism

    Article • Theoretical and Mathematical Physics, April 2013, Springer Science + Business Media

    Dmitry Shirokov

  40. Extension of Pauli’s theorem to Clifford algebras

    Article • Doklady Mathematics, October 2011, Pleiades Publishing Ltd

    Dmitry Shirokov

  41. Development of the Method of Quaternion Typification of Clifford Algebra Elements

    Article • Advances in Applied Clifford Algebras, July 2011, Springer Science + Business Media

    Dmitry Shirokov

  42. Quaternion Typification of Clifford Algebra Elements

    Article • Advances in Applied Clifford Algebras, March 2011, Springer Science + Business Media

    Dmitry Shirokov

  43. A Classification of Lie Algebras of Pseudo-Unitary Groups in the Techniques of Clifford Algebras

    Article • Advances in Applied Clifford Algebras, August 2009, Springer Science + Business Media

    Dmitry Shirokov

  44. Classification of elements of clifford algebras according to quaternionic types

    Article • Doklady Mathematics, August 2009, Pleiades Publishing Ltd

    Dmitry Shirokov

  45. Unitary Spaces on Clifford Algebras

    Article • Advances in Applied Clifford Algebras, March 2008, Springer Science + Business Media

    Dmitry Shirokov