03273nam a22003495a 450000100100000000300120001000500170002200600190003900700150005800800410007302000180011402400210013204000140015307200160016708400150018310000310019824502040022926000820043330000340051533600260054933700260057533800360060134700240063749000390066150600660070052019650076665000210273165000400275270000320279285600320282485600670285657-091109CH-001817-320091109150325.0a fot ||| 0|cr nn mmmmamaa091109e20070531sz fot ||| 0|eng d a978303719532170a10.4171/0322doi ach0018173 7aPBP2bicssc a22-xx2msc1 aHofmann, Karl H.,eauthor.10aThe Lie Theory of Connected Pro-Lie Groupsh[electronic resource] :bA Structure Theory for Pro-Lie Algebras, Pro-Lie Groups, and Connected Locally Compact Groups /cKarl H. Hofmann, Sidney A. Morris3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2007 a1 online resource (693 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aEMS Tracts in Mathematics (ETM)v21 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php 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.07aTopology2bicssc07aTopological groups, Lie groups2msc1 aMorris, Sidney A.,eauthor.40uhttps://doi.org/10.4171/032423cover imageuhttps://www.ems-ph.org/img/books/hofmann_mini.jpg