ON DERIVATIONS, 2-LOCAL OPERATORS, AND CENTRAL EXTENSIONS OF JORDAN-BANACH ALGEBRAS
Vol. 6 No. 8 (2026): Eurasian Journal of Mathematical Theory and Computer Sciences 5-11
Abstract
This article investigates structural properties of Jordan-Banach algebras, with emphasis on continuous derivations, 2-local derivations, and cohomological invariants. We establish that every 2-local derivation on a semi-simple Jordan-Banach algebra with essential socle is a continuous derivation, extending classical results of Šemrl and Ayupov to the non-associative topological setting. Furthermore, we prove that the second continuous cohomology group governs formal rigidity of Jordan-Banach algebras under infinitesimal deformations, and demonstrate that the vanishing of provides an obstruction-free criterion for triviality of central extensions. As applications, we characterize derivations on Jordan spin factors and modular annihilator Jordan-Banach algebras. The results bridge algebraic classification techniques with functional analytic frameworks, offering tools for deformation theory in algebraic quantum mechanics.
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References
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