000			02416nam a22002297a 4500
003			OSt
005			20241210161757.0
008			190424b ||||| |||| 00| 0 eng d
020			_a9780817642594
040			_cTata Book House _aICTS-TIFR
050			_aQA387
100			_aAnthony W. Knapp
245			_aLie groups beyond an introduction
260			_aBoston: _bBirkhauser, _c[c2005]
300			_a812 p
490			_aProgress in Mathematics _vVol. 140
505			_a1. Lie Algebras and Lie Groups 2. Complex Semisimple Lie Algebras 3. Universal Enveloping Algebra 4. Compact Lie Groups 5. Finite-Dimensional Representations 6. Structure Theory of Semisimple Groups 7. Advanced Structure Theory 8. Integration
520			_a Fifty years ago Claude Chevalley revolutionized Lie theory by pub­ lishing his classic Theory of Lie Groups I. Before his book Lie theory was a mixture of local and global results. As Chevalley put it, "This limitation was probably necessary as long as general topology was not yet sufficiently well elaborated to provide a solid base for a theory in the large. These days are now passed:' Indeed, they are passed because Chevalley's book changed matters. Chevalley made global Lie groups into the primary objects of study. In his third and fourth chapters he introduced the global notion of ana­ lytic subgroup, so that Lie subalgebras corresponded exactly to analytic subgroups. This correspondence is now taken as absolutely standard, and any introduction to general Lie groups has to have it at its core. Nowadays "local Lie groups" are a thing of the past; they arise only at one point in the development, and only until Chevalley's results have been stated and have eliminated the need for the local theory. But where does the theory go from this point? Fifty years after Cheval­ ley's book, there are clear topics: E. Cartan's completion ofW. Killing's work on classifying complex semisimple Lie algebras, the treatment of finite-dimensional representations of complex semisimple Lie algebras and compact Lie groups by Cartan and H. Weyl, the structure theory begun by Cartan for real semisimple Lie algebras and Lie groups, and harmonic analysis in the setting of semisimple groups as begun by Cartan and Weyl. --- summary provided by publisher
650			_aMathematics
856			_uhttps://link.springer.com/book/10.1007/978-1-4757-2453-0#toc
942			_2lcc _cBK
999			_c2652 _d2652