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Mosc. Math. J., 2015, Volume 15, Number 4, Pages 609–613 (Mi mmj576)  

This article is cited in 2 scientific papers (total in 2 papers)

On the commutator map for real semisimple Lie algebras

Dmitri Akhiezer

Institute for Information Transmission Problems, 19 B. Karetny per., 127994 Moscow, Russia

Abstract: We find new sufficient conditions for the commutator map of a real semisimple Lie algebra to be surjective. As an application, we prove the surjectivity of the commutator map for all simple algebras except $\mathfrak{su}_{p,q}$ ($p$ or $q>1$), $\mathfrak{so}_{p,p+2}$ ($p$ odd or $p=2$), $\mathfrak u^*_{2m+1}(\mathbb H)$ ($m\ge1$) and $EIII$.

Key words and phrases: Lie algebra, Cartan decomposition.

Funding Agency Grant Number
Deutsche Forschungsgemeinschaft SFB/TR 12
SPP 1388
Supported by SFB/TR 12 and SPP 1388 of the DFG.


DOI: https://doi.org/10.17323/1609-4514-2015-15-4-609-613

Full text: http://www.mathjournals.org/.../2015-015-004-002.html
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Bibliographic databases:

MSC: 17B20
Received: January 14, 2015; in revised form June 7, 2015
Language:

Citation: Dmitri Akhiezer, “On the commutator map for real semisimple Lie algebras”, Mosc. Math. J., 15:4 (2015), 609–613

Citation in format AMSBIB
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\by Dmitri~Akhiezer
\paper On the commutator map for real semisimple Lie algebras
\jour Mosc. Math.~J.
\yr 2015
\vol 15
\issue 4
\pages 609--613
\mathnet{http://mi.mathnet.ru/mmj576}
\crossref{https://doi.org/10.17323/1609-4514-2015-15-4-609-613}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3438823}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000368530900002}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. J. Malkoun, N. Nahlus, “Commutators and Cartan subalgebras in Lie algebras of compact semisimple Lie groups”, J. Lie Theory, 27:4 (2017), 1027–1032  mathscinet  isi
    2. N. L. Gordeev, B. È. Kunyavskiǐ, E. B. Plotkin, “Geometry of word equations in simple algebraic groups over special fields”, Russian Math. Surveys, 73:5 (2018), 753–796  mathnet  crossref  crossref  adsnasa  isi  elib
  • Moscow Mathematical Journal
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