Download E-books The Lie Theory of Connected Pro-Lie Groups (EMS Tracts in Mathematics) PDF
By Karl H. Hofmann and Sidney A. Morris
Lie teams have been brought in 1870 by means of the Norwegian mathematician Sophus Lie. A century later Jean Dieudonné quipped that Lie teams had moved to the guts of arithmetic and that one can't adopt whatever with out them. If a whole topological crew $G$ will be approximated via Lie teams within the experience that each id local $U$ of $G$ features a common subgroup $N$ such that $G/N$ is a Lie team, then it truly is referred to as a pro-Lie team. each in the neighborhood compact hooked up topological team and each compact workforce is a pro-Lie staff. whereas the category of in the community compact teams isn't closed less than the formation of arbitrary items, the category of pro-Lie teams is. For part a century, in the community compact pro-Lie teams have drifted during the literature, but this is often the 1st publication which systematically treats the Lie and constitution conception of pro-Lie teams regardless of neighborhood compactness. This examine matches rather well into the present pattern which addresses infinite-dimensional Lie teams. the result of this article are according to a concept of pro-Lie algebras which parallels the constitution idea of finite-dimensional actual Lie algebras to an remarkable measure, although it has needed to conquer higher technical stumbling blocks. This ebook exposes a Lie idea of attached pro-Lie teams (and accordingly of hooked up in the community compact teams) and illuminates the manifold ways that their constitution thought reduces to that of compact teams at the one hand and of finite-dimensional Lie teams at the different. it's a continuation of the authors' primary monograph at the constitution of compact teams (1998, 2006) and is a useful instrument for researchers in topological teams, Lie concept, harmonic research, and illustration conception. it really is written to be available to complex graduate scholars wishing to review this attention-grabbing and significant region of present learn, which has such a lot of fruitful interactions with different fields of arithmetic.
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