people define haar measure to be left invariant,Weil define module of a automorphism to be the quoient of aX and X,where aX denote X changed under operation “a",if it is left invariant,should module always be trival?
A naive question on Haar measure and the module of automorphism
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fourier-analysis
1 Answers
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Haar measure is invariant on one side, so translate on the other side for this. It is a matter of convention which side to use for which. In the commutative case (or discrete case, or compact case) Haar measure is invariant on both sides, so then it is trivial.
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0Indeed, A.Weil only considers the module of locally compact commutative groups. It seems quite contradictory to me... Any help is appreciated, thanks. – 2011-11-18