In physics, this is why we call the derivative operator the "generator of translations"pic.twitter.com/iqJoydnylt
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It's true in the sense that the differentiation operator is the vector in the Lie algebra of the general linear group that generates the one parameter subgroup of translations.
I’m it sure I would say that the derivative operator generates GL(n)..
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That's not what I said. I said it generates a 1-parameter subgroup of Gl(V) where V is a suitably chosen infinite dimensional space of functions on R.
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