Hardcover ISBN:  9783985470488 
Product Code:  EMSTM/36 
List Price:  $129.00 
AMS Member Price:  $103.20 
Hardcover ISBN:  9783985470488 
Product Code:  EMSTM/36 
List Price:  $129.00 
AMS Member Price:  $103.20 

Book DetailsEMS Tracts in MathematicsVolume: 36; 2023; 840 ppMSC: Primary 22
Lie groups were introduced in 1870 by the Norwegian mathematician Sophus Lie. A century later Jean Dieudonn quipped that Lie groups had moved to the center of mathematics and that one cannot undertake anything without them.
A proLie group is a complete topological group \(G\) in which every identity neighborhood \(U\) of \(G\) contains a normal subgroup \(N\) such that the quotient \(G/N\) is a Lie group. Every locally compact connected topological group and every compact group is a proLie group. While the class of locally compact groups is not closed under the formation of arbitrary products, the class of proLie groups is.
For half a century, locally compact proLie groups have drifted through the literature; yet this is the first book which systematically treats the Lie theory and the structure theory of proLie groups irrespective of local compactness. So it fits very well into that current trend which addresses infinite dimensional Lie groups. The results of this text are based on a theory of proLie algebras which parallels the structure theory of finite dimensional real Lie algebras to an astonishing degree even though it has to overcome technical obstacles.
A topological group is said to be almost connected if the quotient group of its connected components is compact. This book exposes a Lie theory of almost connected proLie groups (and hence of almost connected locally compact groups) and illuminates the variety of 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, therefore, a continuation of the authors' monograph on the structure of compact groups (1998, 2006, 2014, 2020, 2023) 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 research, which has so many fruitful interactions with other fields of mathematics.
A publication of the European Mathematical Society (EMS). Distributed within the Americas by the American Mathematical Society.
ReadershipGraduate students and researchers interested in abstract algebra, group theory, and Lie theory.

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Lie groups were introduced in 1870 by the Norwegian mathematician Sophus Lie. A century later Jean Dieudonn quipped that Lie groups had moved to the center of mathematics and that one cannot undertake anything without them.
A proLie group is a complete topological group \(G\) in which every identity neighborhood \(U\) of \(G\) contains a normal subgroup \(N\) such that the quotient \(G/N\) is a Lie group. Every locally compact connected topological group and every compact group is a proLie group. While the class of locally compact groups is not closed under the formation of arbitrary products, the class of proLie groups is.
For half a century, locally compact proLie groups have drifted through the literature; yet this is the first book which systematically treats the Lie theory and the structure theory of proLie groups irrespective of local compactness. So it fits very well into that current trend which addresses infinite dimensional Lie groups. The results of this text are based on a theory of proLie algebras which parallels the structure theory of finite dimensional real Lie algebras to an astonishing degree even though it has to overcome technical obstacles.
A topological group is said to be almost connected if the quotient group of its connected components is compact. This book exposes a Lie theory of almost connected proLie groups (and hence of almost connected locally compact groups) and illuminates the variety of 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, therefore, a continuation of the authors' monograph on the structure of compact groups (1998, 2006, 2014, 2020, 2023) 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 research, which has so many fruitful interactions with other fields of mathematics.
A publication of the European Mathematical Society (EMS). Distributed within the Americas by the American Mathematical Society.
Graduate students and researchers interested in abstract algebra, group theory, and Lie theory.