Laboratory Staff Publications

Publications by the laboratory staff are presented from the moment of the laboratory's foundation (2024 – present) and for several previous years.

2025

1. D. S. Shirokov, “On Grade Automorphism in Ternary Clifford Algebras”, Hypercomplex Analysis and Its Applications. ICHAA 2024 (Aveiro, Portugal, March 18-22, 2024), Trends in Mathematics, 9, eds. Faustino, N., Ferreira, M., Kähler, U., Vieira, N., Birkhäuser, Cham, 2025, 143–150 https://doi.org/10.1007/978-3-031-86858-0_15
2. D. S. Shirokov, “On SU(3) in Ternary Clifford Algebra”, Advances in Computer Graphics. CGI 2024 (Geneva, Switzerland, July 1–5, 2024), Lecture Notes in Computer Science, 15340, eds. Magnenat-Thalmann, N., Kim, J., Sheng, B., Deng, Z., Thalmann, D., Li, P., Springer, Cham, 2025, 336–348 https://doi.org/10.1007/978-3-031-82024-3_26
3. E. R. Filimoshina, D. S. Shirokov, “Generalized Degenerate Clifford and Lipschitz Groups”, Advances in Computer Graphics. CGI 2024 (Geneva, Switzerland, July 1–5, 2024), Lecture Notes in Computer Science, 15340, eds. Magnenat-Thalmann, N., Kim, J., Sheng, B., Deng, Z., Thalmann, D., Li, P., Springer, Cham, 2025, 364–376 https://doi.org/10.1007/978-3-031-82024-3_28
4. S. V. Rumyantseva, D. S. Shirokov, “On Multidimensional Dirac-Hestenes Equation in Geometric Algebra”, Advances in Computer Graphics. CGI 2024 (Geneva, Switzerland, July 1–5, 2024), Lecture Notes in Computer Science, 15340, eds. Magnenat-Thalmann, N., Kim, J., Sheng, B., Deng, Z., Thalmann, D., Li, P., Springer, Cham, 2025, 323–335 https://doi.org/10.1007/978-3-031-82024-3_25
5. H. Sharma, D. S. Shirokov, “Determinant, Characteristic Polynomial, and Inverse in Commutative Analogues of Clifford Algebras”, Advances in Applied Clifford Algebras, 35 (2025), 44 , 22 pp. https://doi.org/10.1007/s00006-025-01406-6, arXiv: 2412.20135
6. D. S. Shirokov, “Calculation of Spin Group Elements Revisited”, International Journal of Geometric Methods in Modern Physics, 2025 https://doi.org/10.1142/S0219887825400316, arXiv: 2412.02772
7. D. S. Shirokov, “On Rank of Multivectors in Geometric Algebras”, Mathematical Methods in the Applied Sciences, 48:11 (2025), 11095–11102 https://doi.org/10.1002/mma.10946, arXiv: 2412.02681
8. S. V. Rumyantseva, D. S. Shirokov, “Introducing Multidimensional Dirac-Hestenes Equation”, Advances in Applied Clifford Algebras, 35 (2025), 24, 20 pp. https://doi.org/10.1007/s00006-025-01382-x, arXiv: 2411.04214
9. D. S. Shirokov, “On Unitary Groups in Ternary and Generalized Clifford Algebras”, Advances in Applied Clifford Algebras, 35 (2025), 25, 19 pp. https://doi.org/10.1007/s00006-025-01388-5, arXiv: 2504.19689
10. H. Sharma, D. S. Shirokov, “On Commutative Analogues of Clifford Algebras and Their Decompositions”, 2025, 28 pp., arXiv: 2504.19763
11. E. R. Filimoshina, D. S. Shirokov, “Generalized Degenerate Clifford and Lipschitz Groups in Geometric Algebras”, Advances in Applied Clifford Algebras, 35 (2025), 29, 35 pp. https://doi.org/10.1007/s00006-025-01390-x, arXiv: 2505.07106
12. E. R. Filimoshina, D. S. Shirokov, “Equivariant Neural Networks with Geometric Algebras: A New Approach”, 2025 International Joint Conference on Neural Networks (IJCNN) (Rome, Italy), IEEE, 2025, 1–8, https://doi.org/10.1109/IJCNN64981.2025.11227310
13. E. R. Filimoshina, D. S. Shirokov, “GLGENN: A Novel Parameter-Light Equivariant Neural Networks Architecture Based on Clifford Geometric Algebras”, Proceedings of the 42nd International Conference on Machine Learning (Vancouver, Canada, 2025), Proceedings of Machine Learning Research, 267, 2025, 17153-17188 https://proceedings.mlr.press/v267/filimoshina25a.html, arXiv: 2506.09625
14. K. S. Abdulkhaev, D. S. Shirokov, “Explicit Formula for Inverse and Determinant in Geometric Algebras over Seven-dimensional Vector Spaces”, Advances in Computer Graphics. CGI 2025 (Hong Kong, July 14–18, 2025), Lecture Notes in Computer Science, Springer, Cham, 2025 (to appear)
15. N. G. Marchuk, “Classification of Field Equations for Weyl and Elko Spinors”, Differential Equations, 61, 338–345 (2025). https://doi.org/10.1134/S0012266125030061
16. N. G. Marchuk, “Conservative Equations in Field Theory: Conservation and Symmetry Laws”, Differential Equations, 61, 872–892 (2025). https://doi.org/10.1134/S0012266125060060
17. N. G. Marchuk, Sketch of a gauge model of gravity with SU(2) symmetry on a Lorentzian manifold with tetrad, 2025, 30 pp., arXiv: 2501.13112
18. S. V. Rumyantseva, Asymptotic expansion of solutions of the 2nd order difference equations in an unbounded domain, Acta Applicandae Mathematicae. 2025. Vol. 195. Article 4 https://doi.org/10.1007/s10440-025-00706-0
19. S. V. Rumyantseva, D. S. Shirokov, “Lorentz Invariance of the Multidimensional Dirac–Hestenes Equation”, Advances in Applied Clifford Algebras, 2025 (to appear)

2024

1. E. R. Filimoshina, D. S. Shirokov, “On generalization of Lipschitz groups and spin groups”, Mathematical Methods in the Applied Sciences, 47:3 (2024), 1375–1400 https://doi.org/10.1002/mma.8530, arXiv: 2205.06045
2. E. R. Filimoshina, D. S. Shirokov, “On some Lie groups in degenerate geometric algebras”, Advanced Computational Applications of Geometric Algebra. ICACGA 2022 (Denver, CO, USA, October 2-5, 2022), Lecture Notes in Computer Science, 13771, eds. Silva, D.W., Hitzer, E., Hildenbrand, D., Springer, Cham, 2024, 186–198 https://doi.org/10.1007/978-3-031-34031-4_16
3. D. S. Shirokov, “On Singular Value Decomposition and Polar Decomposition in Geometric Algebras”, Advances in Computer Graphics. CGI 2023 (Shanghai, August 28 – September 1, 2023), Lecture Notes in Computer Science, 14498, eds. Sheng, B., Bi, L., Kim, J., Magnenat-Thalmann, N., Thalmann, D., Springer, Cham, 2024, 391–401 https://doi.org/10.1007/978-3-031-50078-7_31
4. D. S. Shirokov, “On SVD and Polar Decomposition in Real and Complexified Clifford Algebras”, Advances in Applied Clifford Algebras, 34 (2024), 23, 20 pp. https://doi.org/10.1007/s00006-024-01328-9, arXiv: 2404.11920
5. E. R. Filimoshina, D. S. Shirokov, “A Note on Centralizers and Twisted Centralizers in Clifford Algebras”, Advances in Applied Clifford Algebras, 34 (2024), 50, 22 pp. https://doi.org/10.1007/s00006-024-01345-8, arXiv: 2404.15169
6. D. S. Shirokov, “Noncommutative Vieta theorem in Clifford geometric algebras”, Mathematical Methods in the Applied Sciences, 47:14 (2024), 11305–11320 https://doi.org/10.1002/mma.9221, arXiv: 2301.06848
7. N. G. Marchuk, “A class of field equations for neutrinos with nonzero masses”, Theoret. and Math. Phys., 219:3 (2024), 897–912 https://doi.org/10.1134/S0040577924060023
8. E. V. Vybornyi, S. V. Rumyantseva, Tunneling with Oscillating Effect of Ground States of a Quadratic Operator on a Hyperboloid. Math Notes 116, 1233–1248 (2024). https://doi.org/10.1134/S0001434624110312

2023

1. D. S. Shirokov, “On Noncommutative Vieta Theorem in Geometric Algebras”, Empowering Novel Geometric Algebra for Graphics and Engineering. ENGAGE 2022 (Virtual Event, September 12, 2022), Lecture Notes in Computer Science, 13862, eds. Hitzer, E., Papagiannakis, G., Vasik, P., Springer, Cham, 2023, 28–37 https://doi.org/10.1007/978-3-031-30923-6_3
2. E. R. Filimoshina, D. S. Shirokov, “On Some Lie Groups in Degenerate Clifford Geometric Algebras”, Advances in Applied Clifford Algebras, 33 (2023), 44, 29 pp. https://doi.org/10.1007/s00006-023-01290-y, arXiv: 2301.06842
3. D. S. Shirokov, “Development of the method of averaging in Clifford geometric algebras”, Mathematics, 11:16 (2023), 3607, 18 pp. https://doi.org/10.3390/math11163607, arXiv: 1409.8163
4. D. S. Shirokov, “Classification of all constant solutions of SU(2) Yang–Mills equations with arbitrary current in pseudo-Euclidean space R^{p,q}”, Modern Physics Letters A, 38:20n21 (2023), 2350096, 54 pp. https://doi.org/10.1142/S0217732323500967, arXiv: 1912.04996
5. D. S. Shirokov, On constant solutions of SU(2) Yang–Mills–Dirac equations, 2023, 19 pp., arXiv: 2207.12313
6. D. S. Shirokov, Some algebraic-geometric methods in field theory and other applications [Doctoral dissertation, HSE University, in Russian], 2023, 304 pp. https://elibrary.ru/item.asp?id=74046009
7. N. G. Marchuk, Field Theory Equations and Clifford Algebras [2nd ed., expanded and revised, in Russian]. URSS. 344 pp., 2023. https://urss.ru/cgi-bin/db.pl?lang=RU&blang=ru&page=Book&id=302823

2022

1. D. S. Shirokov, “Hyperbolic Singular Value Decomposition in the Study of Yang–Mills and Yang–Mills–Proca Equations”, Computational Mathematics and Mathematical Physics, 62:6 (2022), 1007–1019 https://doi.org/10.1134/S0965542522060136
2. K. S. Abdulkhaev, D. S. Shirokov, “Basis-free Formulas for Characteristic Polynomial Coefficients in Geometric Algebras”, Advances in Applied Clifford Algebras, 32 (2022), 57, 27 pp. https://doi.org/10.1007/s00006-022-01232-0, arXiv: 2205.13449
3. E. V. Vybornyi, S. V. Rumyantseva, Semiclassical Asymptotics of Oscillating Tunneling for a Quadratic Hamiltonian on the Algebra. Math Notes 112, 642–655 (2022) https://doi.org/10.1134/S0001434622110025

2021

1. D. S. Shirokov, “On inner automorphisms preserving fixed subspaces of Clifford algebras”, Advances in Applied Clifford Algebras, 31 (2021), 30, 23 pp. https://doi.org/10.1007/s00006-021-01135-6, arXiv: 2011.08287
2. D. S. Shirokov, “A note on the hyperbolic singular value decomposition without hyperexchange matrices”, Journal of Computational and Applied Mathematics, 391 (2021), 113450 https://doi.org/10.1016/j.cam.2021.113450, arXiv: 1812.02460
3. D. S. Shirokov, “A note on subspaces of fixed grades in Clifford algebras”, 9th International Conference on Mathematical Modeling: Dedicated to the 75th Anniversary of Professor V.N. Vragov, ISBN: 978-0-7354-4072-2 (Yakutsk, Russia, July 27 - August 1, 2020), AIP Conference Proceedings, 2328, AIP Publishing, 2021, 060001 https://doi.org/10.1063/5.0042103
4. D. S. Shirokov, “On computing the determinant, other characteristic polynomial coefficients, and inverse in Clifford algebras of arbitrary dimension”, Computational and Applied Mathematics, 40 (2021), 173, 29 pp. https://doi.org/10.1007/s40314-021-01536-0, arXiv: 2005.04015
5. D. S. Shirokov, “Basis-free solution to Sylvester equation in Clifford algebra of arbitrary dimension”, Advances in Applied Clifford Algebras, 31 (2021), 70, 19 pp. https://doi.org/10.1007/s00006-021-01173-0, arXiv: 2109.01816
6. K. S. Abdulkhaev, D. S. Shirokov, “On Explicit Formulas for Characteristic Polynomial Coefficients in Geometric Algebras”, Advances in Computer Graphics. CGI 2021 (Virtual Event, September 6–10, 2021), Lecture Notes in Computer Science, 13002, eds. N. Magnenat-Thalmann et al., Springer, Cham, 2021, 670–681 https://doi.org/10.1007/978-3-030-89029-2_50
7. D. S. Shirokov, “On solutions of the Yang-Mills equations in the algebra of h-forms”, International Conference «Marchuk Scientific Readings 2021» (MSR-2021) (4-8 October 2021, Novosibirsk, Russian Federation), Journal of Physics: Conference Series, 2099, IOP Publishing, 2021, 012015 https://doi.org/10.1088/1742-6596/2099/1/012015
8. N. G. Marchuk, “Sketch of a gauge model of gravity with SU(2)SU(2) symmetry in Minkowski space”, Adv. Appl. Clifford Algebr., 31 (2021), 75, 14 pp. https://doi.org/10.1007/s00006-021-01166-z

2020

1. D. S. Shirokov, “On constant solutions of SU(2) Yang-Mills equations with arbitrary current in Euclidean space R^n”, Journal of Nonlinear Mathematical Physics, 27:2 (2020), 199–218 https://doi.org/10.1080/14029251.2020.1700625, arXiv: 1804.04620
2. N. G. Marchuk, D. S. Shirokov, “Local Generalization of Pauli`s Theorem”, Azerb. J. Math., 10:1 (2020), 38–56 https://azjm.org/volumes/1001/pdf/1001-3.pdf, arXiv: 1201.4985
3. N. G. Marchuk, D. S. Shirokov, “On some equations modeling the Yang-Mills equations”, Physics of Particles and Nuclei, 51:4 (2020), 589–594 https://doi.org/10.1134/S1063779620040498
4. N. G. Marchuk, D. S. Shirokov, Theory of Clifford Algebras and Spinors [in Russian]. KRASAND (URSS), 2020, 560 pp. http://urss.ru/cgi-bin/db.pl?lang=Ru&blang=ru&page=Book&id=263794
5. D. S. Shirokov, “On Basis-Free Solution to Sylvester Equation in Geometric Algebra”, Advances in Computer Graphics. CGI 2020 (Geneva, Switzerland, October 20–23, 2020), Lecture Notes in Computer Science, 12221, eds. Magnenat-Thalmann N. et al., Springer, Cham, 2020, 541–548 https://doi.org/10.1007/978-3-030-61864-3_46
6. N. G. Marchuk, “Model Dirac and Dirac–Hestenes Equations as Covariantly Equipped Systems of Equations”, Continuum Mechanics, Applied Mathematics and Scientific Computing: Godunovs Legacy, A liber Amicorum to Professor Godunov, eds. Demidenko, G.V., Romenski, E., Toro, E., Dumbser, M., Springer, 2020, 269–276 https://doi.org/10.1007/978-3-030-38870-6_35
7. N. G. Marchuk, “One Class of Relativistically Invariant First-Order Equations”, Differ. Equ., 56:12 (2020), 1575–1586 https://doi.org/10.1134/S001226612012006X