\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.
Anatoliy P. Petravchuk
1
;
Oleksandr G. Iena
2
,
3
1
Taras Shevchenko University, Faculty of Mechanics and Mathematics, 64 Volodymyrska Street, 01033 Kyiv, Ukraine
2
Technische Universität, Fachbereich Mathematik, Postfach 3049, 67653 Kaiserslautern, Germany
3
Permanent Address: Taras Shevchenko University, Faculty of Mechanics and Mathematics, 64 Volodymyrska Street, 01033 Kyiv, Ukraine
Anatoliy P. Petravchuk; Oleksandr G. Iena. On Centralizers of Elements in the Lie Algebra of the Special Cremona Group SA2(k). Journal of Lie Theory, Tome 16 (2006) no. 3, pp. 561-567. http://geodesic.mathdoc.fr/item/JOLT_2006_16_3_a7/
@article{JOLT_2006_16_3_a7,
author = {Anatoliy P. Petravchuk and Oleksandr G. Iena},
title = {On {Centralizers} of {Elements} in the {Lie} {Algebra} of the {Special} {Cremona} {Group} {SA\protect\textsubscript{2}(k)}},
journal = {Journal of Lie Theory},
pages = {561--567},
year = {2006},
volume = {16},
number = {3},
url = {http://geodesic.mathdoc.fr/item/JOLT_2006_16_3_a7/}
}
TY - JOUR
AU - Anatoliy P. Petravchuk
AU - Oleksandr G. Iena
TI - On Centralizers of Elements in the Lie Algebra of the Special Cremona Group SA2(k)
JO - Journal of Lie Theory
PY - 2006
SP - 561
EP - 567
VL - 16
IS - 3
UR - http://geodesic.mathdoc.fr/item/JOLT_2006_16_3_a7/
ID - JOLT_2006_16_3_a7
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%0 Journal Article
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%A Oleksandr G. Iena
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%J Journal of Lie Theory
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%N 3
%U http://geodesic.mathdoc.fr/item/JOLT_2006_16_3_a7/
%F JOLT_2006_16_3_a7
