How can I picture antisymmetry of the Lie derivative? - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-18T12:53:30Z http://mathoverflow.net/feeds/question/108494 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/108494/how-can-i-picture-antisymmetry-of-the-lie-derivative How can I picture antisymmetry of the Lie derivative? Caleb Weinreb 2012-09-30T21:42:06Z 2012-09-30T21:54:17Z <p>It's obvious that the Lie derivative defined in terms of Lie brackets is anti-symmetric. But what is an intuitive way to visualize the anti-symmetry in the 'differentiating along a flow' definition? </p> <p>Thanks!</p> http://mathoverflow.net/questions/108494/how-can-i-picture-antisymmetry-of-the-lie-derivative/108496#108496 Answer by Qiaochu Yuan for How can I picture antisymmetry of the Lie derivative? Qiaochu Yuan 2012-09-30T21:54:17Z 2012-09-30T21:54:17Z <p>Whichever definition you use that involves differentiating along a flow, it ought to have the property that \$L_X X = 0\$; in other words, for reasons that should be clear, the Lie derivative is alternating. In the presence of bilinearity, this is equivalent to antisymmetry. </p>