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101 0 $aeng
135   $aurnn|mmmmamaa
181   $ctxt$2rdacontent
182   $cc$2rdamedia
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200 10$aThe Lie Theory of Connected Pro-Lie Groups$b[electronic resource] $eA Structure Theory for Pro-Lie Algebras, Pro-Lie Groups, and Connected Locally Compact Groups /$fKarl H. Hofmann, Sidney A. Morris
210 3 $aZuerich, Switzerland $cEuropean Mathematical Society Publishing House$d2007
215   $a1 online resource (693 pages)
225 0 $aEMS Tracts in Mathematics (ETM)$v2
330   $aLie groups were introduced in 1870 by the Norwegian mathematician Sophus Lie. A century later Jean Dieudonne? 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.
517   $aLie Theory of Connected Pro-Lie Groups 
606   $aTopology$2bicssc
606   $aTopological groups, Lie groups$2msc
615 07$aTopology
615 07$aTopological groups, Lie groups
686   $a22-xx$2msc
700   $aHofmann$b Karl H.$0725876
702   $aMorris$b Sidney A.
801  0$bch0018173
906   $aBOOK
912   $a9910151936203321
996   $aThe Lie Theory of Connected Pro-Lie Groups$92565022
997   $aUNINA