Difference between revisions of "Engel algebra"
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| − | An associative algebra or Lie algebra | + | An [[associative algebra]] or [[Lie algebra]] $\mathfrak{g}$ satisfying the Engel condition: For every $X \in \mathfrak{g}$ the inner derivation $\mathrm{ad}\,X$ (cf. [[Derivation in a ring]]) is nilpotent. In other words, all elements of an Engel algebra are [[Engel element]]s, see also [[Lie algebra, nil]]). |
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Latest revision as of 18:39, 16 October 2016
An associative algebra or Lie algebra $\mathfrak{g}$ satisfying the Engel condition: For every $X \in \mathfrak{g}$ the inner derivation $\mathrm{ad}\,X$ (cf. Derivation in a ring) is nilpotent. In other words, all elements of an Engel algebra are Engel elements, see also Lie algebra, nil).
How to Cite This Entry:
Engel algebra. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Engel_algebra&oldid=15350
Engel algebra. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Engel_algebra&oldid=15350
This article was adapted from an original article by Yu.A. Bakhturin (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article