000			03583nam a22006135i 4500
001			978-0-387-49158-5
003			DE-He213
005			20161121231123.0
007			cr nn 008mamaa
008			100301s2007 xxu| s |||| 0|eng d
020			_a9780387491585 _9978-0-387-49158-5
024	7		_a10.1007/978-0-387-49158-5 _2doi
050		4	_aQA252.3
050		4	_aQA387
072		7	_aPBG _2bicssc
072		7	_aMAT014000 _2bisacsh
072		7	_aMAT038000 _2bisacsh
082	0	4	_a512.55 _223
082	0	4	_a512.482 _223
245	1	0	_aCompact Lie Groups _h[electronic resource] / _cedited by Mark R. Sepanski.
264		1	_aNew York, NY : _bSpringer New York, _c2007.
300			_aXIII, 201 p. _bonline resource.
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
347			_atext file _bPDF _2rda
490	1		_aGraduate Texts in Mathematics, _x0072-5285 ; _v235
505	0		_aCompact Lie Groups -- Representations -- HarmoniC Analysis -- Lie Algebras -- Abelian Lie Subgroups and Structure -- Roots and Associated Structures -- Highest Weight Theory.
520			_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.
650		0	_aMathematics.
650		0	_aAssociative rings.
650		0	_aRings (Algebra).
650		0	_aMatrix theory.
650		0	_aAlgebra.
650		0	_aTopological groups.
650		0	_aLie groups.
650		0	_aMathematical analysis.
650		0	_aAnalysis (Mathematics).
650		0	_aDifferential geometry.
650	1	4	_aMathematics.
650	2	4	_aTopological Groups, Lie Groups.
650	2	4	_aLinear and Multilinear Algebras, Matrix Theory.
650	2	4	_aAssociative Rings and Algebras.
650	2	4	_aDifferential Geometry.
650	2	4	_aAnalysis.
700	1		_aSepanski, Mark R. _eeditor.
710	2		_aSpringerLink (Online service)
773	0		_tSpringer eBooks
776	0	8	_iPrinted edition: _z9780387302638
830		0	_aGraduate Texts in Mathematics, _x0072-5285 ; _v235
856	4	0	_uhttp://dx.doi.org/10.1007/978-0-387-49158-5
912			_aZDB-2-SMA
950			_aMathematics and Statistics (Springer-11649)
999			_c508887 _d508887