2012 | OriginalPaper | Buchkapitel
Erlangen Program at Large: An Overview
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This is an overview of the
Erlangen Program at Large
. Study of objects and properties, which are invariant under a group action, is very fruitful far beyond traditional geometry. In this paper we demonstrate this on the example of the group SL
2
(ℝ). Starting from the conformal geometry we develop analytic functions and apply these to functional calculus. Finally we link this to quantum mechanics and conclude by a list of open problems.