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Journal of Lie Theory 16 (2006), No. 3, 561--567
Copyright Heldermann Verlag 2006



On Centralizers of Elements in the Lie Algebra of the Special Cremona Group SA2(k)

Anatoliy P. Petravchuk
Taras Shevchenko University, Faculty of Mechanics and Mathematics, 64 Volodymyrska Street, 01033 Kyiv, Ukraine
aptr@univ.kiev.ua

Oleksandr G. Iena
Technische Universitšt, Fachbereich Mathematik, Postfach 3049, 67653 Kaiserslautern, Germany
Permanent Address: Taras Shevchenko University, Faculty of Mechanics and Mathematics, 64 Volodymyrska Street, 01033 Kyiv, Ukraine
yena@mathematik.uni-kl.de



[Abstract-pdf]

\def\div{\mathop{\rm div}\nolimits} \def\Der{\mathop{\rm Der}\nolimits} We give a description of maximal abelian subalgebras and centralizers of elements in the Lie algebra $sa_2(k)=\{D\in \Der k[x,y] \mid \div D = 0\}$ over an algebraically closed field $k$ of characteristic $0$. This description is given in terms of closed polynomials.

Keywords: Lie algebra, derivation, closed polynomial maximal abelian subalgebra.

MSC: 17B65, 17B05

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