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Izv. Vyssh. Uchebn. Zaved. Mat., 2018, Number 4, Pages 33–48 (Mi ivm9347)  

This article is cited in 1 scientific paper (total in 1 paper)

Foundations of a theory of dual Lie algebras

V. V. Gorbatsevich

Moscow Aviation Institute (National Research University), 3 Orshanskaya str., Moscow, 121552 Russia

Abstract: In this paper we introduce and study dual Lie algebras—Lie algebras over algebra of dual numbers. We prove some fundamental properties of such Lie algebras and track their parallels with properties of usual real and complex Lie algebras. We discuss some results about classification of dual Lie algebra of small dimension and specify connection with the approximate Lie algebras.

Keywords: Lie algebra, algebra of dual numbers, dual Lie algebra, approximate Lie algebra.

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English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2018, 62:4, 29–41

Bibliographic databases:

UDC: 512.554
Received: 09.02.2017

Citation: V. V. Gorbatsevich, “Foundations of a theory of dual Lie algebras”, Izv. Vyssh. Uchebn. Zaved. Mat., 2018, no. 4, 33–48; Russian Math. (Iz. VUZ), 62:4 (2018), 29–41

Citation in format AMSBIB
\Bibitem{Gor18}
\by V.~V.~Gorbatsevich
\paper Foundations of a theory of dual Lie algebras
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2018
\issue 4
\pages 33--48
\mathnet{http://mi.mathnet.ru/ivm9347}
\transl
\jour Russian Math. (Iz. VUZ)
\yr 2018
\vol 62
\issue 4
\pages 29--41
\crossref{https://doi.org/10.3103/S1066369X18040047}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000429242100004}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85045098988}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. V. V. Gorbatsevich, “Dual and almost-dual homogeneous spaces”, Izv. Math., 83:1 (2019), 20–48  mathnet  crossref  crossref  adsnasa  isi  elib
  • Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
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