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Erlangen Program at Large: An Overview

  • Vladimir V. KisilEmail author
Conference paper
Part of the Trends in Mathematics book series (TM)

Abstract

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 SL2(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.

Keywords

Special linear group Hardy space Clifford algebra elliptic parabolic hyperbolic complex numbers dual numbers double numbers splitcomplex numbers Cauchy-Riemann-Dirac operator Möbius transformations functional calculus spectrum quantum mechanics non-commutative geometry. 

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© Springer Basel 2012

Authors and Affiliations

  1. 1.School of MathematicsUniversity of LeedsLeedsUK

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