Journal of Lie Theory

no. 3
On Centralizers of Elements in the Lie Algebra of the Special Cremona Group SA2(k)
Journal of Lie Theory, Volume 16 (2006) no. 3, pp. 561-567
\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.
DOI: 10.5802/jolt.424
Classification: 17B65, 17B05
Keywords: Lie algebra, derivation, closed polynomial maximal abelian subalgebra 
@article{JOLT_2006_16_3_a7,
     author = {A. P. Petravchuk and O. 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},
     doi = {10.5802/jolt.424},
     zbl = {1132.17010},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.424/}
}
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A. P. Petravchuk; O. G. Iena. On Centralizers of Elements in the Lie Algebra of the Special Cremona Group SA2(k). Journal of Lie Theory, Volume 16 (2006) no. 3, pp. 561-567. doi: 10.5802/jolt.424

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