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An Elementary Introduction to Lie Groups

These notes grew out from some informal lectures which the first author gave in the seminar of Prof. Sommer (Inst. f ¨ ur Informatik, Cognitive Systeme, Christian Albrechts Universit¨at Kiel). The lectures were meant for non-mathematicians which had from theirworking background a special interest in these things. The content of these lectures was not fixed from the beginning but they were strongly influenced by the discussions with the audiance in the seminar. During a week in spring 2003, the first author was invited by Prof. Rita Vincenti for an Erasmus Visit to the University of Perugia. Using the material of Kiel, he gave five lectures on an elementary introduction to Lie groups. A listener of these lectures, the second author, took notes, worked it over and made a latex file from it. Some time later, both authors met a week at Kiel University, and brought the notes to the final form. Though the lectures are now in a written form, it is not strictly a scientific text but it is still informal. The aim of the notes is to give students or interested people from other fields a very first glimps to some elementary notions of Lie groups and Lie algebras and their connection. The examples of the text may possibly help to start reading some book on Lie groups. 1

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