Profesor Titular | University of Cadiz | Spain
José María Sánchez-Delgado is an accomplished mathematician and researcher whose work spans the intricate domains of mathematical physics, algebraic geometry, and operator theory. His primary research explores the deep structural relationships among Lie algebras, graded Lie-Rinehart algebras, and symplectic Lie superalgebras, as well as the decomposition of linear operators in pre-Euclidean spaces. These topics represent fundamental pillars in the study of mathematical frameworks that describe physical systems, geometric symmetries, and analytical transformations.Sánchez-Delgado’s research contributions have significantly enriched the understanding of graded algebraic systems and their applications to modern geometry and physics. His studies on Lie-Rinehart algebras expand the algebraic foundations that connect derivations and differential operators, offering new approaches to algebraic modeling and geometric representation. Similarly, his investigations into symplectic Lie superalgebras with filiform modules reveal innovative algebraic architectures that enhance comprehension of symmetry principles and structure-preserving transformations in theoretical physics.His publication record, comprising 37 peer-reviewed papers with over 200 citations and an h-index of 8, reflects sustained scholarly influence and consistent intellectual advancement. Notable recent works include “Graded Lie-Rinehart Algebras,” “Quadratic Symplectic Lie Superalgebras with a Filiform Module as an Odd Part,” and “Decomposition of Linear Operators on Pre-Euclidean Spaces by Means of Graphs.” These studies collectively demonstrate his ability to combine abstract algebraic reasoning with geometric intuition and analytical rigor.Sánchez-Delgado’s approach emphasizes the interconnection between algebraic formalism and geometric interpretation, promoting the creation of mathematical tools that are both conceptually elegant and computationally applicable. By employing graph-based decomposition techniques and graded algebraic systems, he provides new perspectives for exploring operator dynamics, metric transformations, and structure-preserving mappings across various mathematical spaces.His collaborative works with international co-authors further contribute to advancing the theoretical landscape of mathematical physics and higher algebra. Through his insightful analyses and innovative methodologies, José María Sánchez-Delgado continues to strengthen the bridge between pure mathematics and applied theoretical sciences, advancing the global understanding of the mathematical structures that govern geometry, symmetry, and physical reality.
Profiles: Scopus | ORCID | Google Scholar
Featured Publications
Calderón Martín, A. J., & Sánchez-Delgado, J. M. (2012). On split Leibniz algebras.
Citations: 56
Calderón Martín, A. J., & Sánchez-Delgado, J. M. (2012). On the structure of split Lie color algebras. Linear Algebra and its Applications, 436(2), 307–315.
Citations: 46
Albuquerque, H., Barreiro, E., Benayadi, S., Boucetta, M., & Sánchez-Delgado, J. M. (2021). Poisson algebras and symmetric Leibniz bialgebra structures on oscillator Lie algebras. Journal of Geometry and Physics, 160, 103939.
Citations: 23
Calderón, A. J., & Sánchez-Delgado, J. M. (2016). The structure of split regular BiHom-Lie algebras. Journal of Geometry and Physics, 110, 296–305.
Citations: 18
Calderón Martín, A. J., & Sánchez-Delgado, J. M. (2012). On the structure of graded Lie superalgebras. Modern Physics Letters A, 27(25), 1250142.
Citations: 16
Dr. José María Sánchez-Delgado’s research advances the theoretical foundations of Lie algebras, Leibniz structures, and Poisson systems, deepening the mathematical understanding that underpins modern physics, quantum theory, and computational modeling. His innovative contributions strengthen the bridge between abstract algebraic theory and real-world applications, fostering global progress in scientific computation, symmetry analysis, and mathematical physics.