On the group of Lie-orthogonal operators on a Lie algebra

Abstract

Finite dimensional Lie algebras over the field of complex numbers with a linear operator $T: L\to L$ such that $[T(x),T(y)]=[x,y]$ for all $x,y\in L$ are studied. The group of such non-degenerative linear operators on $L$ is considered. Some properties of this group and its relations with the group $\operatorname{Aut}(L)$ in the general linear group $GL(L)$ are described.

Full Text

Article Information

Title	On the group of Lie-orthogonal operators on a Lie algebra
Source	Methods Funct. Anal. Topology, Vol. 17 (2011), no. 3, 199-203
MathSciNet	MR2857722
Copyright	The Author(s) 2011 (CC BY-SA)

Authors Information

S. V. Bilun
Kyiv Taras Shevchenko University, 64, Volodymyrska, Kyiv, 01601, Ukraine D.

V. Maksimenko
Kyiv National University of Construction and Architecture, 31, Povitroflotsky avenue, Kyiv, 03680, Ukraine

A. P. Petravchuk
Kyiv Taras Shevchenko University, 64, Volodymyrska, Kyiv, 01601, Ukraine 

Citation Example

S. V. Bilun, D. V. Maksimenko, and A. P. Petravchuk, On the group of Lie-orthogonal operators on a Lie algebra, Methods Funct. Anal. Topology 17 (2011), no. 3, 199-203.

BibTex

@article {MFAT591,
    AUTHOR = {Bilun, S. V. and Maksimenko, D. V. and Petravchuk, A. P.},
     TITLE = {On the group of Lie-orthogonal operators on a Lie algebra},
   JOURNAL = {Methods Funct. Anal. Topology},
  FJOURNAL = {Methods of Functional Analysis and Topology},
    VOLUME = {17},
      YEAR = {2011},
    NUMBER = {3},
     PAGES = {199-203},
      ISSN = {1029-3531},
  MRNUMBER = {MR2857722},
       URL = {http://mfat.imath.kiev.ua/article/?id=591},
}