Kisil, VV orcid.org/0000-0002-6593-6147 (2012) Erlangen Programme at Large: An Overview. In: Rogosin, SV and Koroleva, AA, (eds.) Advances in Applied Analysis. Trends in Mathematics . Birkhäuser Basel , pp. 1-94. ISBN 978-3-0348-0416-5
Abstract
This is an overview of Erlangen Programme at Large. Study of objects and properties, which are invariant under a group action, is very fruitful far beyond the 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.
Metadata
Item Type: | Book Section |
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Authors/Creators: |
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Keywords: | Special linear group, Hardy space, Clifford algebra, elliptic, parabolic, hyperbolic, complex numbers, dual numbers, double numbers, split-complex numbers, Cauchy-Riemann-Dirac operator, M\"obius transformations, functional calculus, spectrum, quantum mechanics, non-commutative geometry |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Pure Mathematics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 08 Sep 2017 13:51 |
Last Modified: | 08 Sep 2017 13:51 |
Published Version: | http://www.springer.com/mathematics/analysis/book/... |
Status: | Published |
Publisher: | Birkhäuser Basel |
Series Name: | Trends in Mathematics |
Identification Number: | 10.1007/978-3-0348-0417-2 |
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Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:111544 |