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Izvestiya: Mathematics, 2022, Volume 86, Issue 2, Pages 252–274
DOI: https://doi.org/10.1070/IM9115 (Mi im9115) 		 
Foundations of Lie theory for $\mathcal E$-structures and some of its applications

V. V. Gorbatsevich
English version PDF (499 kB) Russian version article
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DOI: https://doi.org/10.1070/IM9115
Abstract: We construct an analogue of classical Lie theory in the case of Lie groups and Lie algebras defined over the algebra of dual numbers. As an application, we study approximate symmetries of differential equations and construct analogues of Hjelmslev's natural geometry.
Keywords: dual numbers, Lie theory, Lie theorems, approximate symmetries of differential equations, Hjelmslev's natural geometry.
Received: 01.10.2020
Revised: 15.01.2021
Published: 18.05.2022
Bibliographic databases:
Document Type: Article
UDC: 512.816.5
MSC: 17B05, 30G35, 53C15
Language: English
Original paper language: Russian
Citation: V. V. Gorbatsevich, “Foundations of Lie theory for $\mathcal E$-structures and some of its applications”, Izv. Math., 86:2 (2022), 252–274
Citation in format AMSBIB
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\by V.~V.~Gorbatsevich
\paper Foundations of Lie theory for~$\mathcal E$-structures and some of its applications
\jour Izv. Math.
\yr 2022
\vol 86
\issue 2
\pages 252--274
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