منابع مشابه
Iwasawa decompositions of groups with a root group datum
The Iwasawa decomposition of a connected semisimple complex Lie group or a connected semisimple split real Lie group is one of the most fundamental observations of classical Lie theory. It implies that the geometry of a connected semisimple complex resp. split real Lie group G is controlled by any maximal compact subgroup K. Examples are Weyl’s unitarian trick in the representation theory of Li...
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A root datum is a quadruple L = (L,∆, L,∆) in which (1) L is a free Z-module of finite rank and L is its dual Hom(L,Z); (2) ∆ is a finite subset of L and ∆ is one of L; (3) implicit is a map α 7→ α from ∆ to∆ such that (〈α, β∨〉) is a Cartan matrix. In the literature, this is usually called a based root datum. For my purposes it serves as a better beginning. I’ll say later something about the di...
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H"{o}lder in 1893 characterized all groups of order $pqr$ where $p>q>r$ are prime numbers. In this paper, by using new presentations of these groups, we compute their full automorphism group.
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This paper sets out to discuss ongoing activities in the tide and chart datum components of hydrography and charting. It expands on the paper presented at FIG (Fédération Internationale des Géomètres) in Brighton 1998 by Mr Matt Higgins and is a revised and updated version of the paper Chart Datum for Hydrography by GPS delivered by the present authors to the Survey 99 Congress, Sunshine Coast,...
متن کاملPolish Groups Topological Groups a Topological Group Is a Group G with a Topology on G for Which the Operations
These notes introduce the reader to Polish groups|topological groups in which the underlying space is Polish. No background in topological groups is assumed, but I will present the material fairly rapidly and leave quite a lot for the reader to check on his or her own. My main motivation for writing such notes arises from the applications and connections in model theory, where closed subgroups ...
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ژورنال
عنوان ژورنال: Innovations in Incidence Geometry: Algebraic, Topological and Combinatorial
سال: 2009
ISSN: 2640-7345,2640-7337
DOI: 10.2140/iig.2009.9.5