000			02018 a2200229 4500
008			240820b2003 |||||||| |||| 00| 0 eng d
020			_a9780821827789 (PB)
041			_aeng
080			_a512 _bARV
100			_aArvanitoyeorgos, Andreas
245			_aAn Introduction to Lie Groups and the Geometry of Homogeneous Spaces
260			_bAMS _c2003 _aRhode Island
300			_axvi, 141p.
490			_aStudent mathematical library, 1520-9121 _v22
504			_aIncludes Bibliography (129-137) and index
505			_a1. Lie groups 2. Maximal tori and the classification theorem 3. The geometry of a compact Lie group 4. Homogeneous spaces 5. The geometry of a reductive homogeneous space 6. Symmetric spaces 7. Generalized flag manifolds 8. Advanced topics
520			_aIt is remarkable that so much about Lie groups could be packed into this small book. But after reading it, students will be well-prepared to continue with more advanced, graduate-level topics in differential geometry or the theory of Lie groups. The theory of Lie groups involves many areas of mathematics. In this book, Arvanitoyeorgos outlines enough of the prerequisites to get the reader started. He then chooses a path through this rich and diverse theory that aims for an understanding of the geometry of Lie groups and homogeneous spaces. In this way, he avoids the extra detail needed for a thorough discussion of other topics. Lie groups and homogeneous spaces are especially useful to study in geometry, as they provide excellent examples where quantities (such as curvature) are easier to compute. A good understanding of them provides lasting intuition, especially in differential geometry. The book is suitable for advanced undergraduates, graduate students, and research mathematicians interested in differential geometry and neighboring fields, such as topology, harmonic analysis, and mathematical physics
650			_aHomogeneous spaces
650			_aLie groups
690			_aMathematics
942			_cBK
999			_c60382 _d60382