000			01811nam a22002537a 4500
003			OSt
005			20230715192309.0
008			230714b |||||||| |||| 00| 0 hin d
020			_a9781944660888
040			_aNISER LIBRARY _cNISER LIBRARY
041			_aEnglish
082			_a512.81 _bHSI-L
100			_aHsiang, W. Y.
245			_aLectures on lie groups
260			_aSingapore: _bWorld Scientific, _c2023
300			_av, 108p. _bPbk.
490			_aSeries on university mathematics _vVol. 2
504			_aContents: 1. Linear Groups and Linear Representations 2. Lie Groups and Lie Algebras 3. Orbital Geometry of the Adjoint Action 4. Coxeter Groups, Weyl Reduction and Weyl Formulas 5. Structural Theory of Compact Lie Algebras 6. Classification Theory of Compact Lie Algebras and Compact Connected Lie Groups
520			_aThis invaluable book provides a concise and systematic introduction to the theory of compact connected Lie groups and their representations, as well as a complete presentation of the structure and classification theory. It uses a non-traditional approach and organization. There is a proper balance between, and a natural combination of, the algebraic and geometric aspects of Lie theory, not only in technical proofs but also in conceptual viewpoints. For example, the orbital geometry of adjoint action, is regarded as the geometric organization of the totality of non-commutativity of a given compact connected Lie group, while the maximal tori theorem of É. Cartan and the Weyl reduction of the adjoint action on G to the Weyl group action on a chosen maximal torus are presented as the key results that provide a clear-cut understanding of the orbital geometry.
650			_aMATHEMATICS
650			_aLIE ALGEBRA
650			_aLIE GROUPS
942			_cN _2udc
999			_c34301 _d34301