Natural extension of a Lie algebra A4,18b,|b|≤1, realizations, invariant systems and integrability

Muhammad Ayub and Saira Bano

Applied Mathematics and Computation, 2025, vol. 494, issue C

Abstract: In the frame of Lie theory, the classical successive reduction of order for scalar ODEs is not much effective for system of differential equations due to technical hurdles. Lie algebraic approach is utilized to overcome these hurdles, then further invoked for the classification, linearization and integrability of system of differential equations. But in the case of higher dimension, this approach has also its own limitations due to classification of low dimensional Lie algebras and corresponding realizations. In the realm of Lie algebra theory, a natural extension refers to the process that involves enlarging a Lie algebra by adding new elements or structures while maintaining the fundamental algebraic properties. This extension technique finds applications in various fields, including physics, geometry, and mathematics.

Keywords: Systems of second-order ODEs; Lie algebra; Realizations; Integrability; Linearization (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:494:y:2025:i:c:s0096300325000013

DOI: 10.1016/j.amc.2025.129274

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