03049nam a22005415i 4500001001800000003000900018005001700027007001500044008004100059020001800100024003500118050001400153072001600167072002300183082001200206100004200218245011900260250001100379264004600390300004400436336002600480337002600506338003600532347002400568490001700592505026600609520112000875650001701995650001302012650001802025650002502043650002902068650001302097650002102110650002102131650001702152650001302169650003802182650003302220650005702253650002102310650002102331710003402352773002002386776003602406830001702442856004802459978-0-387-78866-1DE-He21320180115171424.0cr nn 008mamaa100301s2010 xxu| s |||| 0|eng d a97803877886617 a10.1007/978-0-387-78866-12doi 4aQA150-272 7aPBF2bicssc 7aMAT0020002bisacsh04a5122231 aKosmann-Schwarzbach, Yvette.eauthor.10aGroups and Symmetriesh[electronic resource] :bFrom Finite Groups to Lie Groups /cby Yvette Kosmann-Schwarzbach. aFirst. 1aNew York, NY :bSpringer New York,c2010. aXVI, 196 p. 44 illus.bonline resource. atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda1 aUniversitext0 aGeneral Facts About Groups -- Representations of Finite Groups -- Representations of Compact Groups -- Lie Groups and Lie Algebras -- Lie Groups SU(2) and SO(3) -- Representations of SU(2) and SO(3) -- Spherical Harmonics -- Representations of SU(3) and Quarks. aUnlike many other texts, this book deals with the theory of representations of finite groups, compact groups, linear Lie groups and their Lie algebras, concisely and in one volume. Key Topics: • Brisk review of the basic definitions of group theory, with examples • Representation theory of finite groups: character theory • Representations of compact groups using the Haar measure • Lie algebras and linear Lie groups • Detailed study of SO(3) and SU(2), and their representations • Spherical harmonics • Representations of SU(3), roots and weights, with quark theory as a consequence of the mathematical properties of this symmetry group This book is illustrated with portraits and a few historical remarks. With only linear algebra and calculus as prerequisites, Groups and Symmetries: From Finite Groups to Lie Groups is accessible to advanced undergraduates in mathematics and physics, and will still be of interest to beginning graduate students. Exercises for each chapter and a collection of problems with complete solutions make this an ideal text for the classroom and for independent study. 0aMathematics. 0aAlgebra. 0aGroup theory. 0aApplied mathematics. 0aEngineering mathematics. 0aPhysics. 0aQuantum physics. 0aCrystallography.14aMathematics.24aAlgebra.24aGroup Theory and Generalizations.24aApplications of Mathematics.24aTheoretical, Mathematical and Computational Physics.24aQuantum Physics.24aCrystallography.2 aSpringerLink (Online service)0 tSpringer eBooks08iPrinted edition:z9780387788654 0aUniversitext40uhttp://dx.doi.org/10.1007/978-0-387-78866-1