02869nmm a2200385 u 4500001001200000003002700012005001700039007002400056008004100080020001800121100002200139245006900161250001700230260004800247300003300295505017800328653002600506653005100532653003300583653001200616653002300628653003500651653003500686653001800721653003400739653001300773710003400786041001900820989003600839490003400875856007200909082001200981082001100993520147901004EB000355474EBX0100000000000000020852600000000000000.0cr|||||||||||||||||||||130626 ||| eng a97803874915851 aSepanski, Mark R.00aCompact Lie GroupshElektronische Ressourcecby Mark R. Sepanski a1st ed. 2007 aNew York, NYbSpringer New Yorkc2007, 2007 aXIII, 201 pbonline resource0 aCompact Lie Groups -- Representations -- HarmoniC Analysis -- Lie Algebras -- Abelian Lie Subgroups and Structure -- Roots and Associated Structures -- Highest Weight Theory aDifferential Geometry aLinear and Multilinear Algebras, Matrix Theory aGlobal differential geometry aAlgebra aTopological Groups aAssociative Rings and Algebras aTopological Groups, Lie Groups aMatrix theory aGlobal analysis (Mathematics) aAnalysis2 aSpringerLink (Online service)07aeng2ISO 639-2 bSpringeraSpringer eBooks 2005-0 aGraduate Texts in Mathematics uhttps://doi.org/10.1007/978-0-387-49158-5?nosfx=yxVerlag3Volltext0 a512.4820 a512.55 aBlending algebra, analysis, and topology, the study of compact Lie groups is one of the most beautiful areas of mathematics and a key stepping stone to the theory of general Lie groups. Assuming no prior knowledge of Lie groups, this book covers the structure and representation theory of compact Lie groups. Included is the construction of the Spin groups, Schur Orthogonality, the Peter–Weyl Theorem, the Plancherel Theorem, the Maximal Torus Theorem, the Commutator Theorem, the Weyl Integration and Character Formulas, the Highest Weight Classification, and the Borel–Weil Theorem. The necessary Lie algebra theory is also developed in the text with a streamlined approach focusing on linear Lie groups. Key Features: • Provides an approach that minimizes advanced prerequisites • Self-contained and systematic exposition requiring no previous exposure to Lie theory • Advances quickly to the Peter–Weyl Theorem and its corresponding Fourier theory • Streamlined Lie algebra discussion reduces the differential geometry prerequisite and allows a more rapid transition to the classification and construction of representations • Exercises sprinkled throughout This beginning graduate-level text, aimed primarily at Lie Groups courses and related topics, assumes familiarity with elementary concepts from group theory, analysis, and manifold theory. Students, research mathematicians, and physicists interested in Lie theory will find this text very useful