Abstract
In the category of algebras with flat, connections the concepts of symmetries and recursion operators are defined. Lie algebra structure of symmetries is described for the objects of this category possessing recursion operators. In particular, sufficient conditions for existence of infinite series of commuting symmetries are formulated. The results are applied to symmetries of differential equations.
Mathematics Subject Classification (1991): 58F07, 58F35, 58G05.
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Krasil’Shchik, I.S. (1998). Algebras With Flat Connections and Symmetries of Differential Equations. In: Komrakov, B.P., Krasil’shchik, I.S., Litvinov, G.L., Sossinsky, A.B. (eds) Lie Groups and Lie Algebras. Mathematics and Its Applications, vol 433. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-5258-7_25
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DOI: https://doi.org/10.1007/978-94-011-5258-7_25
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