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W2044147924 abstract "Let k be a field of characteristic zero and let B be a graded k -algebra. We obtain information on a given derivation D : B → B by studying the behavior of the associated homogeneous derivation gr D . As an application, we give a complete classification of locally nilpotent derivations D : k [ X , Y , Z ] → k [ X , Y , Z ] satisfying D 2 X = D 2 Y = 0 ; in particular, it is proved that every k -derivation D satisfying D 2 X = D 2 Y = D 2 Z = 0 is essentially a partial derivative." @default.
W2044147924 created "2016-06-24" @default.
W2044147924 creator A5041345629 @default.
W2044147924 date "2005-04-01" @default.
W2044147924 modified "2023-09-26" @default.
W2044147924 title "Homogeneization of locally nilpotent derivations and an application to <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML altimg=si1.gif overflow=scroll><mml:mi>k</mml:mi><mml:mo stretchy=false>[</mml:mo><mml:mi>X</mml:mi><mml:mo>,</mml:mo><mml:mi>Y</mml:mi><mml:mo>,</mml:mo><mml:mi>Z</mml:mi><mml:mo stretchy=false>]</mml:mo></mml:math>" @default.
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W2044147924 doi "https://doi.org/10.1016/j.jpaa.2004.08.006" @default.
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