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001			57-091109
003			CH-001817-3
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008			091109e20070531sz fot ||| 0|eng d
020			_a9783037195321
024	7	0	_a10.4171/032 _2doi
040			_ach0018173
072		7	_aPBP _2bicssc
084			_a22-xx _2msc
100	1		_aHofmann, Karl H., _eauthor.
245	1	0	_aThe Lie Theory of Connected Pro-Lie Groups _h[electronic resource] : _bA Structure Theory for Pro-Lie Algebras, Pro-Lie Groups, and Connected Locally Compact Groups / _cKarl H. Hofmann, Sidney A. Morris
260	3		_aZuerich, Switzerland : _bEuropean Mathematical Society Publishing House, _c2007
264		1	_aZuerich, Switzerland : _bEuropean Mathematical Society Publishing House, _c2007
300			_a1 online resource (693 pages)
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
347			_atext file _bPDF _2rda
490	0		_aEMS Tracts in Mathematics (ETM) _v2
506	1		_aRestricted to subscribers: _uhttp://www.ems-ph.org/ebooks.php
520			_aLie groups were introduced in 1870 by the Norwegian mathematician Sophus Lie. A century later Jean Dieudonné quipped that Lie groups had moved to the center of mathematics and that one cannot undertake anything without them. If a complete topological group G can be approximated by Lie groups in the sense that every identity neighborhood U of G contains a normal subgroup N such that G/N is a Lie group, then it is called a pro-Lie group. Every locally compact connected topological group and every compact group is a pro-Lie group. While the class of locally compact groups is not closed under the formation of arbitrary products, the class of pro-Lie groups is.   For half a century, locally compact pro-Lie groups have drifted through the literature, yet this is the first book which systematically treats the Lie and structure theory of pro-Lie groups irrespective of local compactness. This study fits very well into that current trend which addresses infinite dimensional Lie groups. The results of this text are based on a theory of pro-Lie algebras which parallels the structure theory of finite dimensional real Lie algebras to an astonishing degree even though it has to overcome greater technical obstacles. This book exposes a Lie theory of connected pro-Lie groups (and hence of connected locally compact groups) and illuminates the manifold ways in which their structure theory reduces to that of compact groups on the one hand and of finite dimensional Lie groups on the other. It is a continuation of the authors' fundamental monograph on the structure of compact groups (1998, 2006), and is an invaluable tool for researchers in topological groups, Lie theory, harmonic analysis and representation theory. It is written to be accessible to advanced graduate students wishing to study this fascinating and important area of current research, which has so many fruitful interactions with other fields of mathematics.
650	0	7	_aTopology _2bicssc
650	0	7	_aTopological groups, Lie groups _2msc
700	1		_aHofmann, Karl H., _eauthor.
700	1		_aMorris, Sidney A., _eauthor.
856	4	0	_uhttps://doi.org/10.4171/032
856	4	2	_3cover image _uhttp://www.ems-ph.org/img/books/hofmann_mini.jpg
942			_2EBK13749 _cEBK
999			_c50373 _d50373