Two articles by Dmitry Shirokov on the mirror laboratory project were published in international journals
Two papers by Dmitry Shirokov on the mirror laboratory project 'Quaternions, Geometric Algebras, and Applications' were published in international journals:
- D. S. Shirokov, 'On Rank of Multivectors in Geometric Algebras', Mathematical Methods in the Applied Sciences (WoS Q1), 2025, arXiv: 2412.02681, https://doi.org/10.1002/mma.10946
Abstract: We introduce the notion of rank of multivector in Clifford geometric algebras of arbitrary dimension without using the corresponding matrix representations and using only geometric algebra operations. We use the concepts of characteristic polynomial in geometric algebras and the method of SVD. The results can be used in various applications of geometric algebras in computer science, engineering, and physics.
- D. S. Shirokov, 'Calculation of Spin Group Elements Revisited', International Journal of Geometric Methods in Modern Physics (Scopus Q2), 2025, arXiv: 2412.02772, https://doi.org/10.1142/S0219887825400316
Abstract: In this paper, we present a method for calculation of spin groups elements for known pseudo-orthogonal group elements with respect to the corresponding two-sheeted coverings. We present our results using the Clifford algebra formalism in the case of arbitrary dimension and signature, and then explicitly using matrices, quaternions, and split-quaternions in the cases of all possible signatures (p,q) of space up to dimension n=p+q=3. The different formalisms are convenient for different possible applications in physics, engineering, and computer science.
