000			02488 a2200253 4500
001			135658
003			ISI Library, Kolkata
005			20150413134031.0
008			150325b xxu||||| |||| 00| 0 eng d
020			_a9780691049908
040			_aISI Library
082	0	0	_223 _bC527 _a512.55
100			_aChevalley, Claude.
245			_aTheory of lie groups / _cClaude Chevalley.
260			_aPrinceton : _bPrinceton University Press, _c1999.
300			_a viii, 217 p. ; _c24 cm.
490	0		_aPrinceton mathematical series ; _v8
490	0		_aPrinceton landmarks in mathematics
500			_aIncludes index.
505			_aINTRODUCTION I. THE CLASSICAL LINEAR GROUPS II. TOPOLOGICAL GROUPS III. MANIFOLDS IV. ANALYTIC GROUPS. LIE GROUPS V. THE DIFFERENTIAL CALCULUS 0F CARTAN VI. COMPACT LIE GROUPS AND THEIR REPRESENTATIONS INDEX.
520			_a"This book was the first treatise on Lie groups in which a modern point of view was adopted systematically, namely, that a continuous group can be regarded as a global object. To develop this idea to its fullest extent, Chevalley incorporated a broad range of topics, such as: the covering spaces of topological spaces, analytic manifolds, integration of complete systems of differential equations on a manifold, and the calculus of exterior differential forms." "The book opens with a short description of the classical groups: unitary groups, orthogonal groups, symplectic groups, etc. These special groups are then used to illustrate the general properties of Lie groups, which are considered later. The general notion of a Lie group is defined and correlated with the algebraic notion of a Lie algebra; the subgroups, factor groups, and homomorphisms of Lie groups are studied by making use of the Lie algebra. The last chapter is concerned with the theory of compact groups, culminating in Peter-Weyl's theorem on the existence of representations. Given a compact group, it is shown how one can construct algebraically the corresponding Lie group with complex parameters which appears in the form of a certain algebraic variety (associated algebraic group). This construction is intimately related to the proof of the generalization given by Tannaka of Pontrjagin's duality theorem for Abelian groups." "The continued importance of Lie groups in mathematics and theoretical physics makes this an indispensable volume for researchers in both fields."--Jacket.
650	0		_aLie groups.
942			_2ddc _cBK
999			_c418897 _d418897