03409nam a22004215a 4500001001100000003001200011005001700023006001900040007001500059008004100074020001800115024002100133040001400154072001600168072001600184084003600200245015400236260008200390300003400472336002600506337002600532338003600558347002400594490008300618505093700701506006601638520093801704650003502642650002102677650003102698650004002729650001802769650003102787700002502818700003702843856003202880856007502912191-150427CH-001817-320150427234500.0a fot ||| 0|cr nn mmmmamaa150427e20150430sz fot ||| 0|eng d a978303719648970a10.4171/1482doi ach0018173 7aPBX2bicssc 7aPBM2bicssc a01-xxa22-xxa51-xxa53-xx2msc10aSophus Lie and Felix Klein: The Erlangen Program and Its Impact in Mathematics and Physicsh[electronic resource] /cLizhen Ji, Athanase Papadopoulos3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2015 a1 online resource (348 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aIRMA Lectures in Mathematics and Theoretical Physics (IRMA) ;x2523-5133 ;v2300tSophus Lie, a giant in mathematics /rLizhen Ji --tFelix Klein: his life and mathematics /rLizhen Ji --tKlein and the Erlangen Programme /rJeremy J. Gray --tKlein’s “Erlanger Programm”: do traces of it exist in physical theories? /rHubert Goenner --tOn Klein’s So-called Non-Euclidean geometry /rNorbert A’Campo, Athanase Papadopoulos --tWhat are symmetries of PDEs and what are PDEs themselves? /rAlexandre Vinogradov --tTransformation groups in non-Riemannian geometry /rCharles Frances --tTransitional geometry /rNorbert A’Campo, Athanase Papadopoulos --tOn the projective geometry of constant curvature spaces /rAthanase Papadopoulos, Sumio Yamada --tThe Erlangen program and discrete differential geometry /rYuri B. Suris --tThree-dimensional gravity – an application of Felix Klein’s ideas in physics /rCatherine Meusburger --tInvariances in physics and group theory /rJean-Bernard Zuber.1 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aThe Erlangen program expresses a fundamental point of view on the use of groups and transformation groups in mathematics and physics. The present volume is the first modern comprehensive book on that program and its impact in contemporary mathematics and physics. Klein spelled out the program, and Lie, who contributed to its formulation, is the first mathematician who made it effective in his work. The theories that these two authors developed are also linked to their personal history and to their relations with each other and with other mathematicians, incuding Hermann Weyl, Élie Cartan, Henri Poincaré, and many others. All these facets of the Erlangen program appear in the present volume.
The book is written by well-known experts in geometry, physics and history of mathematics and physics. It is addressed to mathematicians, to graduate students, and to all those interested in the development of mathematical ideas.07aHistory of mathematics2bicssc07aGeometry2bicssc07aHistory and biography2msc07aTopological groups, Lie groups2msc07aGeometry2msc07aDifferential geometry2msc1 aJi, Lizhen,eeditor.1 aPapadopoulos, Athanase,eeditor.40uhttps://doi.org/10.4171/148423cover imageuhttps://www.ems-ph.org/img/books/ji_papadopoulos_mini.jpg