GROUP THEORY Exceptional Lie groups as invariance groups
نویسنده
چکیده
We offer the ultimate birdtracker guide to exceptional Lie groups.
منابع مشابه
Reduction of Differential Equations by Lie Algebra of Symmetries
The paper is devoted to an application of Lie group theory to differential equations. The basic infinitesimal method for calculating symmetry group is presented, and used to determine general symmetry group of some differential equations. We include a number of important applications including integration of ordinary differential equations and finding some solutions of partial differential equa...
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1 Introduction Sometimes a solution to a mathematical problem is so beautiful that it can impede further progress for a whole century. So is the case with the Killing-Cartan classification of semi-simple Lie algebras [Killing 1888; Cartan 1952]. It is elegant, it is beautiful, and it says that the 3 classical families and 5 exceptional algebras are all there is, but what does that mean? The con...
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The theory of Lie groups and representations was developed by Lie, Killing, Cartan, Weyl and others to a degree of quasi-perfection, in the years 1870-1930 . The main topological features of compact simple Lie groups were elucidated in the 40s by H. Hopf, Pontriagin and others. The exceptional groups were studied by Chevalley, Borel, Freudenthal etc. in 1949-1957. Torsion in the exceptional gro...
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Random matrix theory, the exceptional Lie groups, and L-functions. Abstract There has recently been interest in relating properties of matrices drawn at random from the classical compact groups to statistical characteristics of number-theoretical L-functions. One example is the relationship conjectured to hold between the value distributions of the characteristic polynomials of such matrices an...
متن کاملInvariant Differential Equations on Homogeneous Manifolds by Sigurdur Helgason
1. Historical origins of Lie group theory. Nowadays when Lie groups enter in a profound way into so many areas of mathematics, their historical origin is of considerable general interest. The connection between Lie groups and differential equations is not very pronounced in the modern theory of Lie groups, so in this introduction we attempt to describe some of the foundational work of S. Lie, W...
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تاریخ انتشار 2000